He attended the South Cortland district school, Cortland Academy (in Homer) and Oberlin College in Ohio. He taught school in New York, Pennsylvania, and Ohio, studied law, was admitted to the bar in Worcester, Massachusetts in 1840, and practiced for two years in Beloit, Wisconsin.
He returned to New York and settled in Dryden in 1844. Goodrich was elected as a Republican to the Forty-second Congress, holding office from March 4, 1871 to March 3, 1873. He was an unsuccessful candidate for reelection in 1872 to the Forty-third Congress, and resumed the practice of law.
He moved to Auburn, New York in 1875 and continued the practice of law.
He died there in 1881. Interment was in Green Hills Cemetery, Dryden.
He is the great-great-great-grandfather of United States. Secretary of Education Arne Duncan.
He was postmaster of Dryden from October 2, 1849 to June 25, 1853 and was a member of the New York Constitutional Convention in 1867 and 1868.