Born in New York, Farnsworth moved to Buckhannon as a child and worked as a tailor, store owner, and farmer.

A strong Union supporter, Farnsworth played key roles during the Second Wheeling Convention in 1861. He later served in the state legislature and became governor for six days after the first governor, Arthur Boreman, resigned to join the U.S. Senate. He stayed active in politics, supporting workers’ and farmers' rights and speaking out against railroad monopolies. He died in Buckhannon at age 72.