Hendricks was born near Fultonham, Ohio and moved with his parents to Indiana in 1820. His uncle, William Hendricks, was Governor of Indiana from 1822 to 1825. He graduated from Hanover College in 1841, and was admitted to the bar in 1843, practicing in Shelbyville, Indiana. He was a member of the state House of Representatives in 1848, a member of the state constitutional convention, and elected as a Democrat to the thirty-second and Congresses (March 4, 1851 - March 3, 1855). Hendricks was Chairman of the Committee on Mileage and the Committee on Invalid Pensions. He campaigned unsuccessfully for reelection in 1854.

Following his tenure in Congress, Hendricks was Commissioner of the General Land Office from 1855 to 1859, and an unsuccessful Democratic candidate for Governor of Indiana in 1860. He moved to Indianapolis in 1860 and practiced law. He was elected as a Democrat to the United States Senate, and served from March 4, 1863, to March 3, 1869. He was then elected Governor of Indiana in 1872, serving from 1873 until 1877.

Because of the death of Democratic candidate Horace Greeley days after the popular vote in the presidential election of 1872, Hendricks received 42 electoral votes that were previously pledged to Greeley. Hendricks ran as an unsuccessful candidate for Vice President on the Democratic ticket with Samuel Tilden in the following presidential election of 1876. He ran again in U.S. presidential election, 1884, and was elected Vice President of the United States on the Democratic ticket with Grover Cleveland, filling an office that had been vacant since Vice President Chester A. Arthur became President in 1881. He only served from March 4, 1885, until his death a few months later in Indianapolis. He is interred in Crown Hill Cemetery. With his death, the Vice Presidency became vacant until Levi Morton became Vice President in 1889.