He was left an orphan at the age of three and lived with his grandfather Abijah Felch, a veteran of the American Revolution.

[1] He was state auditor general for a few weeks in 1842 before being appointed associate justice of the Michigan Supreme Court in 1842, where he served until his resignation in 1845, after being elected governor.

Felch resigned as governor on March 3, 1847, after being elected by the Michigan legislature as a Democrat to the United States Senate.

He returned to live in Ann Arbor, Michigan, that year and made an unsuccessful attempt at a non-consecutive term as governor against the Republican incumbent Kinsley S. Bingham.

He died at his home in Ann Arbor, Michigan at the age of 91, and is interred at Forest Hill Cemetery along with his wife, Lucretia.