Hendricks was born near Zanesville, Ohio and moved with his parents to Indiana in 1820. 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 Thirty-third Congresses (March 4, 1851 - March 3, 1855). He was an unsuccessful candidate for reelection in 1854. He was Chairman of the Committee on Mileage and the Committee on Invalid Pensions.
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 Governor of Indiana in 1872 and an unsuccessful candidate for Vice President on the Democratic ticket with Samuel Tilden in 1876. He was elected Vice President of the United States in 1884 on the Democratic ticket with Grover Cleveland and served from March 4, 1885 until his death in Indianapolis. He was intered in Crown Hill Cemetery.