Before returning to England, Cook made a final sweep across the South Atlantic from Cape Horn and surveyed, mapped and took possession for Britain of South Georgia, which had been explored by Anthony de la Roché in 1675. Cook also discovered and named Clerke Rocks and the South Sandwich Islands ("Sandwich Land"). He then turned north to South Africa, and from there continued back to England. His reports upon his return home put to rest the popular myth of Terra Australis.

James Cook was born on 7 November 1728 (N.S.) in the village of Marton in Yorkshire and baptised on 14 November (N.S.) in the parish church of St Cuthbert, where his name can be seen in the church register. He was the second of eight children of James Cook, a Scottish farm labourer from Ednam in Roxburghshire, and his locally born wife, Grace Pace, from Thornaby-on-Tees. In 1736, his family moved to Airey Holme farm at Great Ayton, where his father's employer, Thomas Skottowe, paid for him to attend the local school. In 1741, after five years' schooling, he began work for his father, who had been promoted to farm manager. For leisure, he would climb a nearby hill, Roseberry Topping, enjoying the opportunity for solitude. Cooks' Cottage, his parents' last home, which he is likely to have visited, is now in Melbourne, Australia, having been moved from England and reassembled, brick by brick, in 1934.

In 1745, when he was 16, Cook moved 20 miles (32 km) to the fishing village of Staithes, to be apprenticed as a shop boy to grocer and haberdasher william Sanderson. Historians have speculated that this is where Cook first felt the lure of the sea while gazing out of the shop window.

Cook's first posting was with HMS Eagle, serving as able seaman and master's mate under Captain Joseph Hamar for his first year aboard, and Captain Hugh Palliser thereafter. In October and November 1755 he took part in Eagle's capture of one French warship and the sinking of another, following which he was promoted to boatswain in addition to his other duties. His first temporary command was in March 1756 when he was briefly master of Cruizer, a small cutter attached to Eagle while on patrol.

In June 1757 Cook formally passed his master's examinations at Trinity House, Deptford, qualifying him to navigate and handle a ship of the King's fleet. He then joined the frigate HMS Solebay as master under Captain Robert Craig.

During the Seven Years' War, Cook served in North America as master aboard the fourth-rate Navy vessel HMS Pembroke. With others in Pembroke's crew, he took part in the major amphibious assault that captured the Fortress of Louisbourg from the French in 1758, and in the siege of Quebec City in 1759. Throughout his Service he demonstrated a talent for surveying and cartography, and was responsible for mapping much of the entrance to the Saint Lawrence River during the siege, thus allowing General Wolfe to make his famous stealth attack during the 1759 Battle of the Plains of Abraham.

Cook's surveying ability was also put to use in mapping the jagged coast of Newfoundland in the 1760s, aboard HMS Grenville. He surveyed the north-west stretch in 1763 and 1764, the south coast between the Burin Peninsula and Cape Ray in 1765 and 1766, and the west coast in 1767. At this time Cook employed local pilots to point out the "rocks and hidden dangers" along the south and west coasts. During the 1765 season, four pilots were engaged at a daily pay of 4 shillings each: John Beck for the coast west of "Great St Lawrence", Morgan Snook for Fortune Bay, John Dawson for Connaigre and Hermitage Bay, and John Peck for the "Bay of Despair".

Cook married Elizabeth Batts (1742–1835), the daughter of Samuel Batts, keeper of the Bell Inn, Wapping and one of his mentors, on 21 December 1762 at St Margaret's Church, Barking, Essex. The couple had six children: James (1763–94), Nathaniel (1764–80, lost aboard HMS Thunderer which foundered with all hands in a hurricane in the West Indies), Elizabeth (1767–71), Joseph (1768–68), George (1772–72) and Hugh (1776–93), the last of whom died of scarlet fever while a student at Christ's College, Cambridge. When not at sea, Cook lived in the East End of London. He attended St Paul's Church, Shadwell, where his son James was baptised. Cook has no direct descendants—all his children died before having children of their own.

In 1766, the Admiralty engaged Cook to command a scientific voyage to the Pacific Ocean. The purpose of the voyage was to observe and record the transit of Venus across the Sun for the benefit of a Royal Society inquiry into a means of determining longitude. Cook, at the age of 39, was promoted to lieutenant to grant him sufficient status to take the command. For its part the Royal Society agreed that Cook would receive a one hundred guinea gratuity in addition to his Naval pay.

The expedition sailed aboard HMS Endeavour, departing England on 26 August 1768. Cook and his crew rounded Cape Horn and continued westward across the Pacific to arrive at Tahiti on 13 April 1769, where the observations of the Venus Transit were made. However, the result of the observations was not as conclusive or accurate as had been hoped. Once the observations were completed, Cook opened the sealed orders which were additional instructions from the Admiralty for the second part of his voyage: to search the south Pacific for signs of the postulated rich southern continent of Terra Australis. Cook then sailed to New Zealand and mapped the complete coastline, making only some minor errors. He then voyaged west, reaching the south-eastern coast of Australia on 19 April 1770, and in doing so his expedition became the first recorded Europeans to have encountered its eastern coastline.

After his departure from Botany Bay he continued northwards. He stopped at Bustard Bay (now known as Seventeen Seventy or 1770) at 8 o’clock on 23 May 1770. On 24 May Cook and Banks and others went ashore. Continuing north, on 11 June a mishap occurred when HMS Endeavour ran aground on a shoal of the Great Barrier Reef, and then “nursed into a river mouth on 18 June 1770”. The ship was badly damaged and his voyage was delayed almost seven weeks while repairs were carried out on the beach (near the docks of modern Cooktown, Queensland, at the mouth of the Endeavour River). The voyage then continued, sailing through Torres Strait and on 22 August Cook landed on Possession Island, where he claimed the entire coastline that he had just explored as British territory. He returned to England via Batavia (modern Jakarta, Indonesia), where many in his crew succumbed to malaria, and then the Cape of Good Hope, arriving at the island of Saint Helena on 12 July 1771.

Shortly after his return from the first voyage, Cook was promoted in August 1771, to the rank of commander. In 1772 he was commissioned to lead another scientific expedition on behalf of the Royal Society, to search for the hypothetical Terra Australis. On his first voyage, Cook had demonstrated by circumnavigating New Zealand that it was not attached to a larger landmass to the south. Although he charted almost the entire eastern coastline of Australia, showing it to be continental in size, the Terra Australis was believed to lie further south. Despite this evidence to the contrary, Alexander Dalrymple and others of the Royal Society still believed that a massive southern continent should exist.

Cook's voyages were involved in another unusual first. The first recorded circumnavigation of the world by an animal was by Cook's goat, who made that memorable journey twice; the first time on HMS Dolphin, under Samuel Wallis, and then aboard Endeavour. When they returned to England, Cook had the goat presented with a silver collar engraved with lines from Samuel Johnson: Perpetui, ambita bis terra, praemia lactis Haec habet altrici Capra secunda Jovis. (“In fame scarce second to the nurse of Jove,/ This Goat, who twice the world had traversed round,/Deserving both her master's care and love,/Ease and perpetual pasture now has found.”) She was put to pasture on Cook's farm outside London, and was reportedly admitted to the privileges of the Royal Naval hospital at Greenwich. Cook's journal recorded the date of the goat's death: 28 March 1772.

Cook commanded HMS Resolution on this voyage, while Tobias Furneaux commanded its companion ship, HMS Adventure. Cook's expedition circumnavigated the globe at an extreme southern latitude, becoming one of the first to cross the Antarctic Circle (17 January 1773). In the Antarctic fog, Resolution and Adventure became separated. Furneaux made his way to New Zealand, where he lost some of his men during an encounter with Māori, and eventually sailed back to Britain, while Cook continued to explore the Antarctic, reaching 71°10'S on 31 January 1774.

Cook almost encountered the mainland of Antarctica, but turned towards Tahiti to resupply his ship. He then resumed his southward course in a second fruitless attempt to find the supposed continent. On this leg of the voyage he brought a young Tahitian named Omai, who proved to be somewhat less knowledgeable about the Pacific than Tupaia had been on the first voyage. On his return voyage to New Zealand in 1774, Cook landed at the Friendly Islands, Easter Island, Norfolk Island, New Caledonia, and Vanuatu.

Cook succeeded in circumnavigating the world on his first voyage without losing a single man to scurvy, an unusual accomplishment at the time. He tested several preventive measures but the most important was frequent replenishment of fresh food. It was for presenting a paper on this aspect of the voyage to the Royal Society that he was presented with the Copley Medal in 1776. Ever the observer, Cook was the first European to have extensive contact with various people of the Pacific. He correctly postulated a link among all the Pacific peoples, despite their being separated by great ocean stretches (see Malayo-Polynesian languages). Cook theorised that Polynesians originated from Asia, which scientist Bryan Sykes later verified. In New Zealand the coming of Cook is often used to signify the onset of colonisation.

By the second week of August 1778 Cook was through the Bering Strait, sailing into the Chukchi Sea. He headed north-east up the coast of Alaska until he was blocked by sea ice. His furthest north was 70 degrees 44 minutes. Cook then sailed west to the Siberian coast, and then south-east down the Siberian coast back to the Bering Strait. By early September 1778 he was back in the Bering Sea to begin the trip to the Sandwich (Hawaiian) Islands. He became increasingly frustrated on this voyage, and perhaps began to suffer from a stomach ailment; it has been speculated that this led to irrational behaviour towards his crew, such as forcing them to eat walrus meat, which they had pronounced inedible.

Cook's contributions to knowledge were internationally recognised during his lifetime. In 1779, while the American colonies were fighting Britain for their independence, Benjamin Franklin wrote to captains of colonial warships at sea, recommending that if they came into contact with Cook's vessel, they were to "not consider her an enemy, nor suffer any plunder to be made of the effects contained in her, nor obstruct her immediate return to England by detaining her or sending her into any other part of Europe or to America; but that you treat the said Captain Cook and his people with all civility and kindness, ... as Common friends to mankind." Unknown to Franklin, Cook had met his death a month before this safe conduct "passport" was written.

One of the earliest monuments to Cook in the United Kingdom is located at The Vache, erected in 1780 by Admiral Hugh Palliser, a contemporary of Cook and one-time owner of the estate. A huge obelisk was built in 1827 as a monument to Cook on Easby Moor overlooking his boyhood village of Great Ayton, along with a smaller monument at the former location of Cook's cottage. There is also a monument to Cook in the church of St Andrew the Great, St Andrew's Street, Cambridge, where his sons Hugh, a student at Christ's College, and James were buried. Cook's widow Elizabeth was also buried in the church and in her will left money for the memorial's upkeep. The 250th anniversary of Cook's birth was marked at the site of his birthplace in Marton, by the opening of the Captain Cook Birthplace Museum, located within Stewart Park (1978). A granite vase just to the south of the museum marks the approximate spot where he was born. Tributes also abound in post-industrial Middlesbrough, including a primary school, shopping square and the Bottle 'O Notes, a public artwork by Claes Oldenburg, that was erected in the town's Central Gardens in 1993. Also named after Cook is the James Cook University Hospital, a major teaching hospital which opened in 2003 with a railway station serving it called James Cook opening in 2014. The Royal Research Ship RRS James Cook was built in 2006 to replace the RRS Charles Darwin in the UK's Royal Research Fleet, and Stepney Historical Trust placed a plaque on Free Trade Wharf in the Highway, Shadwell to commemorate his life in the East End of London. In 2002 Cook was placed at number 12 in the BBC's poll of the 100 Greatest Britons.

Several officers who served under Cook went on to distinctive accomplishments. william Bligh, Cook's sailing master, was given command of HMS Bounty in 1787 to sail to Tahiti and return with breadfruit. Bligh is most known for the mutiny of his crew which resulted in his being set adrift in 1789. He later became governor of New South Wales, where he was subject of another mutiny—the Rum Rebellion was the only successful armed takeover of an Australian government. George Vancouver, one of Cook's midshipmen, led a voyage of exploration to the Pacific Coast of North America from 1791 to 1794. In honour of his former commander, Vancouver's ship was named Discovery. George Dixon, who sailed under Cook on his third expedition, later commanded his own. A lieutenant under Cook, Henry Roberts, spent many years after that voyage preparing the detailed charts that went into Cook's posthumous Atlas, published around 1784.

The Australian Museum acquired its "Cook Collection" in 1894 from the Government of New South Wales. At that time the collection consisted of 115 artefacts collected on Cook's three voyages throughout the Pacific Ocean, during the period 1768–80, along with documents and memorabilia related to these voyages. Many of the ethnographic artefacts were collected at a time of first contact between Pacific Peoples and Europeans. In 1935 most of the documents and memorabilia were transferred to the Mitchell Library in the State Library of New South Wales. The provenance of the collection shows that the objects remained in the hands of Cook's widow Elizabeth Cook, and her descendants, until 1886. In this year John Mackrell, the great-nephew of Isaac Smith, Elizabeth Cook's cousin, organised the display of this collection at the request of the NSW Government at the Colonial and Indian Exhibition in London. In 1887 the London-based Agent-General for the New South Wales Government, Saul Samuel, bought John Mackrell's items and also acquired items belonging to the other relatives Reverend Canon Frederick Bennett, Mrs Thomas Langton, H. M. C. Alexander, and william Adams. The collection remained with the Colonial Secretary of NSW until 1894, when it was transferred to the Australian Museum.

A US coin, the 1928 Hawaiian Sesquicentennial half dollar carries Cook's image. Minted for the 150th anniversary of his discovery of the islands, its low mintage (10,008) has made this Example of Early United States commemorative coins both scarce and expensive. The site where he was killed in Hawaii was marked in 1874 by a white obelisk set on 25 square feet (2.3 m) of chained-off beach. This land, although in Hawaii, was deeded to the United Kingdom. A nearby town is named Captain Cook, Hawaii; several Hawaiian businesses also carry his name. The Apollo 15 Command/Service Module Endeavour was named after Cook's ship, HMS Endeavour, as was the space shuttle Space Shuttle Endeavour. Another shuttle, Discovery, was named after Cook's HMS Discovery.

The first institution of higher education in North Queensland, Australia was named after him, with James Cook University opening in Townsville in 1970. In Australian rhyming slang the expression "Captain Cook" means "look". Numerous institutions, landmarks and place names reflect the importance of Cook's contributions, including the Cook Islands, the Cook Strait, Cook Inlet, and the Cook crater on the Moon. Aoraki/Mount Cook, the highest summit in New Zealand, is named for him. Another Mount Cook is on the border between the US state of Alaska and the Canadian Yukon Territory, and is designated Boundary Peak 182 as one of the official Boundary Peaks of the Hay–Herbert Treaty. A life-size statue of Cook upon a column stands in a park in the centre of Sydney.

Cook gathered accurate longitude measurements during his first voyage due to his navigational skills, the help of Astronomer Charles Green and by using the newly published Nautical Almanac tables, via the lunar distance method—measuring the angular distance from the moon to either the sun during daytime or one of eight bright stars during night-time to determine the time at the Royal Observatory, Greenwich, and comparing that to his local time determined via the altitude of the sun, moon, or stars. On his second voyage Cook used the K1 chronometer made by Larcum Kendall, which was the shape of a large pocket watch, 5 inches (13 cm) in diameter. It was a copy of the H4 clock made by John Harrison, which proved to be the first to keep accurate time at sea when used on the ship Deptford's journey to Jamaica, 1761–62.