Bragg was born at Westward near Wigton, Cumberland, the son of Robert John Bragg, a merchant marine officer and farmer, and his wife Mary née Wood, a clergyman's daughter. When Bragg was seven years old, his mother died, and he was raised by his uncle, also named william Bragg, at Market Harborough, Leicestershire. He was educated at the Grammar School there, at King William's College on the Isle of Man and, having won an exhibition (scholarship), at Trinity College, Cambridge. He graduated in 1884 as third wrangler, and in 1885 was awarded a first class honours in the mathematical tripos.

In 1885, at the age of 23, Bragg was appointed (Sir Thomas) Elder Professor of Mathematics and Experimental Physics in the University of Adelaide, and started work there early in 1886. Being a skilled Mathematician, at that time he had limited knowledge of physics, most of which was in the form of applied mathematics he had learnt at Trinity. Also at that time, there were only about a hundred students doing full courses at Adelaide, of whom less than a handful belonged to the science school, whose deficient teaching facilities Bragg improved by apprenticing himself to a firm of instrument makers. Bragg was an able and popular lecturer; he encouraged the formation of the student union, and the attendance, free of charge, of science teachers at his lectures.

In 1889 in Adelaide, W.H. Bragg married Gwendoline Todd, a skilled water-colour Painter, and daughter of Astronomer, Meteorologist and electrical Engineer Sir Charles Todd. They had three children, a daughter, Gwendolen and two sons, (William) Lawrence (W.L.) and Robert. Robert was killed in the Battle of Gallipoli. W.H.'s wife Gwendoline died in 1929. W.H. Bragg died in 1942 in England and was survived by his daughter Gwendolen (Mrs. Alban Caroe) and his son, Sir Lawrence Bragg.

Bragg's interest in physics developed, particularly in the field of electromagnetism. In 1895 he was visited by Ernest Rutherford, en route from New Zealand to Cambridge; this was the commencement of a lifelong friendship. Bragg had a keen interest in the new discovery of Wilhelm Röntgen. On 29 May 1896 at Adelaide, Bragg demonstrated before a meeting of local doctors the application of "X-rays to reveal structures that were otherwise invisible". Samuel Barbour, senior Chemist of F. H. Faulding & Co., an Adelaide pharmaceutical manufacturer, supplied the necessary apparatus in the form of a Crookes tube, a glass discharge tube. The tube had been obtained at Leeds, England, where Barbour visited the firm of Reynolds and Branson, a manufacturer of photographic and laboratory equipment. Barbour returned to Adelaide in April 1896. Barbour had conducted his own experiments shortly after return to Australia, but results were limited due to limited battery power. At the University, the tube was attached to an induction coil and a battery borrowed from Sir Charles Todd, Bragg's father-in-law. The induction coil was utilized to produce the electric spark necessary for Bragg and Barbour to "generate short bursts of X-rays". The audience was favorably impressed. Bragg availed himself as a test subject, in the manner of Röntgen and allowed an X-ray photograph to be taken of his hand. The image of the fingers in his hand revealed "an old injury to one of his fingers sustained when using the turnip chopping machine on his father's farm in Cumbria".

As early as 1895 Professor william H. (later Sir William) Bragg was working on wireless telegraphy, though public lectures and demonstrations focussed on his X-ray research which would later lead to his Nobel Prize. In a hurried visit by Rutherford, he was reported as working on a Hertzian oscillator. There were many Common practical threads to the two technologies and he was ably assisted in the laboratory by Arthur Lionel Rogers who manufactured much of the equipment. On 21 September 1897 Bragg gave the first recorded public demonstration of the working of wireless telegraphy in Australia during a lecture meeting at the University of Adelaide as part of the Public Teachers' Union conference. Bragg departed Adelaide in December 1897, and spent all of 1898 on a 12-month leave of absence, touring Great Britain and Europe and during this time visited Marconi and inspected his wireless facilities. He returned to Adelaide in early March 1899, and already on 13 May 1899 Bragg and his father-in-law, Sir Charles Todd, were conducting preliminary tests of wireless telegraphy with a transmitter at the Observatory and a receiver on the South Road (about 200 metres). Experiments continued throughout the southern winter of 1899 and the range was progressively extended to Henley Beach. In September the work was extended to two way transmissions with the addition of a second induction coil loaned by Mr. Oddie of Ballarat. It was desired to extend the experiments cross a sea path and Todd was interested in connecting Cape Spencer and Althorpe Island, but local costs were considered prohibitive while the charges for patented equipment from the Marconi Company were exorbitant. At the same time Bragg's interests were leaning towards X-rays and practical work in wireless in South Australia was largely dormant for the next decade.

The turning-point in Bragg's career came in 1904 when he gave the presidential address to section A of the Australasian Association for the Advancement of Science at Dunedin, New Zealand, on "Some Recent Advances in the Theory of the Ionization of Gases". This idea was followed up "in a brilliant series of researches" which, within three years, earned him a fellowship of the Royal Society of London. This paper was also the origin of his first book Studies in Radioactivity (1912). Soon after the delivery of his 1904 address, some radium bromide was made available to Bragg for experimentation. In December 1904 his paper "On the Absorption of α Rays and on the Classification of the α Rays from Radium" appeared in the Philosophical Magazine, and in the same issue a paper "On the Ionization Curves of Radium", written in collaboration with his student Richard Kleeman, also appeared.

Bragg was elected Fellow of the Royal Society in 1907, vice-president in 1920, and served as President of the Royal Society from 1935 to 1940. Elected member of the Royal Academy of Science, Letters and Fine Arts of Belgium on 1.6.1946.

At the end of 1908 Bragg returned to England. During his 23 years in Australia "he had seen the number of students at the University of Adelaide almost quadruple, and had a full share in the development of its excellent science school."

Bragg occupied the Cavendish chair of physics in the University of Leeds from 1909. He continued his work on X-rays with much success. He invented the X-ray spectrometer and with his son, Lawrence Bragg, then a research student at Cambridge, founded the new science of X-ray crystallography, the analysis of crystal structure using X-ray diffraction.

Both of his sons were called into the army after war broke out in 1914 . The following year he was appointed Quain Professor of physics at University College London. He had to wait for almost a year to contribute to the war effort: finally in July 1915 he was appointed to the Board of Invention and Research set up by the Admiralty. In September his younger son Robert died of wounds at Gallipoli. In November he shared the Nobel Prize in Physics with elder son william Lawrence. The Navy was struggling to prevent sinkings by unseen, submerged U boats. The Scientists recommended that the best tactic was to Listen for the submarines. The Navy had a hydrophone research establishment at Aberdour Scotland, staffed with navy men. In November 1915 two young physicists were added to its staff. Bowing to outside pressure for using science, in July 1916 the Admiralty appointed Bragg as scientific Director at Aberdour, assisted by three additional young physicists. They developed an improved directional hydrophone, which convinced the Admiralty of their usefulness. Late in 1916 Bragg with his small group moved to Harwich, where the staff was enlarged and they had access to a submarine for tests. In France, where Scientists had been mobilized since the beginning of the war, the Physicist Paul Langevin made a major stride with echolocation, generating intense sound pulses with quartz sheets oscillated at high frequency, which were then used as microphones to Listen for echoes. Quartz was usable when vacuum tubes became available at the end of 1917 to amplify the faint signals. The British made sonar practicable by using mosaics of small quartz bits rather than slices from a large crystal. In January 1918 Bragg moved into the Admiralty as head of scientific research in the anti-submarine division. By war's end British vessels were being equipped with sonar manned by trained listeners.

William H. Bragg was appointed Commander of the Order of the British Empire (CBE) in 1917 and Knight Commander (KBE) in 1920. He was admitted to the Order of Merit in 1931.

From 1923 he was Fullerian Professor of Chemistry at the Royal Institution and Director of the Davy Faraday Research Laboratory. This institution was practically rebuilt in 1929–30 and, under Bragg's directorship many valuable papers were issued from the laboratory. In 1919, 1923 and 1925 he was invited to deliver the Royal Institution Christmas Lecture on The World of Sound; Concerning the Nature of Things and Old Trades and New Knowledge respectively.

Bragg was elected President of the Royal Society in 1935. The Physiologist AV Hill was Biological Secretary and soon ACG Egerton became Physical Secretary. During World War I all three had stood by for frustrating months before their skills were employed for the war effort. Now the cause of science was strengthened by the report of a high level Army committee on lessons learned in the last war; their first recommendation was to "keep abreast of modern scientific developments". Anticipating another war, the Ministry of Labour was persuaded to accept Hill as a consultant on scientific manpower. The Royal Society compiled a register of qualified men. They proposed a small committee on science to advise the Committee on Imperial Defence, but this was rejected. Finally in 1940, as Bragg's term ended, a Scientific Advisory Committee to the War Cabinet was appointed. Bragg died in 1942.

In 1962, the Bragg Laboratories were constructed at the University of Adelaide to commemorate 100 years since the birth of Sir william H. Bragg.

The lecture theatre of King William's College (KWC) is named in memory of Bragg; the Sixth-Form invitational literary debating society at KWC, the Bragg Society, is also named in his memory. One of the school "Houses" at Robert Smyth School, Market Harborough, Leicester, is named "Bragg" in memory of him being a student there. Since 1992, the Australian Institute of Physics has awarded The Bragg Gold Medal for Excellence in Physics for the best PhD thesis by a student at an Australian university. The two sides of the medal contain the images of Sir william Henry and his son Sir Lawrence Bragg.