Hendricks was born on September 7, 1819, in Muskingum County, Ohio, near East Fultonham and Zanesville. He was the second of eight children born to John and Jane (Thomson) Hendricks, who were originally from Pennsylvania.

In 1820 Hendricks moved with his parents and older brother to Madison in Jefferson County, Indiana, at the urging of Thomas's uncle, william Hendricks, a successful Politician who served as a U.S. Representative, a U.S. Senator (1825–37), and as the third governor of Indiana (1822–25). Thomas's family first settled on a farm near his uncle's home in Madison, and moved to Shelby County, Indiana, in 1822. Hendricks's father, a successful farmer who operated a general store, became involved in politics, including appointment from President Andrew Jackson as deputy surveyor of public lands for his district. Indiana's Democratic Party Leaders frequently visited the Hendricks home in Shelbyville, and from an early age Hendricks was influenced to enter politics.

One of Hendricks's lasting legacies during his tenure as governor began with discussion to fund construction of a new Indiana Statehouse. The existing structure, which had been in use since 1835, had become too small, forcing the growing state government to rent additional buildings around Indianapolis. Besides its size, the dilapidated capitol building was in need of major repair. The roof in the Hall of Representatives had collapsed in 1867 and public inspectors condemned the building in 1873. The cornerstone for the present-day state capital building was laid in 1880, after Hendricks left office, and he delivered the keynote speech at the ceremony. The new statehouse was completed eight years later and remains in use as Indiana's state capitol building.

Hendricks remained active in the legal community and in state and national politics from the 1840s until his death in 1885.

Hendricks attended local schools (Shelby County Seminary and Greensburg Academy). He graduated from Hanover College in Hanover, Indiana, in 1841, in the same class as Albert G. Porter, also a Future governor of Indiana. After college Hendricks read law with Judge Stephen Major in Shelbyville, and in 1843 he took an eight-month law course at a school operated by his uncle, Judge Alexander Thomson in Chambersburg, Pennsylvania. Hendricks returned to Indiana, was admitted to the bar in 1843, and established a private practice in Shelbyville.

In addition to his years of Service in various political offices in Indiana and Washington, D.C., Hendricks maintained an active law practice, which he first established in Shelbyville in 1843 and continued after his relocation to Indianapolis. Hendricks and Oscar B. Hord established a law firm in 1862, where Hendricks practiced until the Indiana General Assembly elected him to represent Indiana in the U.S. Senate in 1863. The law practice was renamed Hendricks, Hord, and Hendricks in 1866, after Abram W. Hendricks joined the firm. In 1873 it was renamed Baker, Hord, and Hendricks, after Conrad Baker, the outgoing governor of Indiana, joined the firm and Hendricks succeeded him as governor. In 1888 the firm passed to Baker's son, who partnered with Edward Daniels, and it became known as Baker & Daniels, which grew into one of the state's leading law firms.

Hendricks married Eliza Carol Morgan of North Bend, Ohio, on September 26, 1845, after a two-year courtship. The couple met when Eliza was visiting her married sister, Mrs. Daniel West, in Shelbyville. The couple's only child, a son named Morgan, was born on January 16, 1848, and died in 1851, at the age of three. Thomas and Eliza Hendricks moved to Indianapolis in 1860 and resided from 1865 to 1872 at 1526 South New Jersey Street, now known as the Bates-Hendricks House.

Hendricks began his political career in 1848, when he served a one-year term in the Indiana House of Representatives after defeating Martin M. Ray, the Whig candidate. Hendricks was also one of the two Shelby County delegates to the 1850–51 Indiana constitutional convention. He served on committee that created the organization of the state's townships and counties and decided on the taxation and financial portion of the state constitution. Hendricks also debated the clauses on the powers of the different offices and argued in favor of a powerful judiciary and the abolishment of grand juries.

Hendricks represented Indiana as a Democrat in the U.S. House of Representatives (1851–55) in the Thirty-second and Thirty-third Congresses from March 4, 1851 to March 3, 1855. Hendricks was chairman of the U.S. Committee on Mileage (Thirty-second Congress) and served on the U.S. Committee on Invalid Pensions (Thirty-third Congress). He supported the principle of popular sovereignty and voted in favor of the Kansas-Nebraska Act of 1854, which expanded slavery into the western territories of the United States. Both positions were unpopular in Hendricks's home district in Indiana and led to defeat in his re-election bid to Congress in 1854.

In 1855 President Franklin Pierce appointed Hendricks as commissioner of the General Land Office in Washington, D.C. His job supervising 180 clerks and a four-year backlog of work was a demanding one, especially at a time when westward expansion meant that the government was going through one of its largest periods of land sales. During his tenure, the land office issued 400,000 land patents and settled 20,000 disputed land cases. Although Hendricks made thousands of decisions related to disputed land claims, only a few were reversed in court, but he did receive some criticism: "He was the first commissioner who apparently had no background or qualifications for the job. ...Some of the rulings and letters during Hendricks's tenure were not always correct."

Hendricks resigned as land office commissioner in 1859 and returned to Shelby County, Indiana. The cause of his departure was not recorded, but potential reasons may have been differences of opinion with President James Buchanan, Pierce's successor. Hendricks resisted Buchanan's efforts to make land office clerks patronage positions, objected to the pro-slavery policies of the Buchanan administration, and supported the homestead bill, which Buchanan opposed.

In 1860 Hendricks, who ran with David Turpie as his running mate, lost to the Republican candidates, Henry S. Lane and Oliver P. Morton. Three of the four men (Lane, Morton, and Hendricks) eventually served as Indiana's governor, and all four became U.S. senators.

Hendricks represented Indiana in the U.S. Senate (1863–69) during the final years of the American Civil War and part of the Reconstruction Era. Military reverses in the Civil War, some unpopular decisions in the Lincoln administration, and Democratic control of the Indiana General Assembly helped Hendricks win election to the U.S. Senate. His six years in the Senate covered the Thirty-eighth, Thirty-ninth, and Fortieth Congresses, where Hendricks was a leader of the small Democratic minority and a member of the opposition who was often overruled.

Hendricks was one of four vice-presidential candidates from Indiana who were elected during the period 1868 to 1920, when Indiana's electoral votes were critical to winning a national election. (The three other men from Indiana who became U.S. vice Presidents during this period were Schuyler Colfax, Charles W. Fairbanks, and Thomas R. Marshall.) Five other men from Indiana, George Washington Julian, Joseph Lane, Judge Samuel Williams, John W. Kern, and william Hayden English, lost their bids for the vice presidency during this time period.

In 1872 Hendricks was elected as the governor of Indiana in his third bid for the office. An indication of Hendricks's growing national popularity occurred during the presidential election of 1872; the Democrats nominated Horace Greeley, the Liberal Republican candidate. Greeley died soon after the election, but before the Electoral College cast its ballots; 42 of 63 Democratic electors previously pledged to Greeley voted for Hendricks.

Although Hendricks succeeded in encouraging legislation enacting election and judiciary reform, the Republican-controlled legislature prevented him from achieving many of his other legislative goals. In 1873 Hendricks signed the Baxter bill, a controversial piece of temperance legislation that established a strict form of local option, even though he personally had favored a licensing law. Hendricks signed the legislation because he thought the bill was constitutional and reflected the majority view of the Indiana General Assembly and the will of Indiana's citizens. The law proved to be unenforceable and was repealed in 1875; it was replaced by a licensing system that Hendricks had preferred.

In the disputed presidential election of 1876 Hendricks ran as the Democratic candidate for vice President with New York governor Samuel Tilden as the party's presidential nominee. Hendricks did not attend the Democratic convention in Saint Louis, but the party was pursuing the strategy of carrying the Solid South along with New York and Indiana. The Indiana delegation urged Hendricks as the vice presidential nominee, and he was nominated unanimously.

As chairman of the Indiana delegation, Hendricks attended the Democratic Party's national convention in 1884 in Chicago, where he was again nominated as its vice presidential candidate by a unanimous vote. Grover Cleveland was the party's presidential nominee in the 1884 presidential election; once again the Democrats' strategy was to win New York, Cleveland's home state, and Hendricks's home state of Indiana, plus the electoral votes of the Solid South. Democrats narrowly won New York, Indiana, and two more Northern states plus the Solid South to secure the election.

Hendricks died unexpectedly on November 25, 1885, during a trip home to Indianapolis. He complained of feeling ill the morning of November 24, went to bed early, and died in his sleep the following day.