Bingham was born to the farmer family of Calvin and Betsy (Scott) Bingham in Camillus, New York in Onondaga County. He attended the common schools and studied law in Syracuse. He moved to Green Oak Township, Michigan in 1833 where he was admitted to the bar and began a private practice. He also engaged in agricultural pursuits and held a number of local offices including justice of the peace, postmaster, and first judge of the probate court of Livingston County.

Bingham became a member of the Michigan State House of Representatives in 1837, was reelected four times and served as Speaker of the House in 1838, 1839, and 1842. He was elected as a Democratic Representative from Michigan's 3rd District to the 30th and 31st Congresses from March 4, 1847 to March 3, 1851. He served as chairman of the Committee on Expenditures in the Department of State in the 31st Congress. He was instrumental in securing approval for building the Beaver Island Head Lighthouse on the south end of Beaver Island in Lake Michigan. He was strongly opposed to the expansion of slavery and was one of minority of Democrats who supported the Wilmot Proviso.

He was not a candidate for re-election in 1850 and resumed agricultural pursuits and affiliated himself with the Free Soil Party.

Bingham was elected as the first Republican Governor of Michigan in 1854 and was re-elected in 1856. He was known as the farmer-governor of Michigan and was instrumental in establishing the Agricultural College of the State of Michigan (today, Michigan State University) and other educational institutions. He was a delegate to the Republican National Convention from Michigan in 1856.

Bingham was elected as a Republican to the United States Senate in 1858 and served in the 36th and 37th Congresses from March 4, 1859, until his death on October 5, 1861. He was as chairman of the Committee on Enrolled Bills in the 37th Congress. He campaigned actively for the election of U.S. President Abraham Lincoln in 1860.

He died in Green Oak and is interred in Old Village Cemetery, Brighton, Michigan.

In 1833, while still in New York, Bingham married Margaret Warden, who had recently moved with her brother Robert Warden and family from Scotland. In 1834 their only child, Kinsley W. Bingham (1838-1908), was born, and Margaret died four days later. In 1839 Bingham married Mary Warden, the younger sister of his first wife, and in 1840 their only child was born, James W. Bingham (1840-1862).

There are three townships named for him in Michigan: