He was born in Salem, Massachusetts and graduated from Yale in 1809. He was a tutor at the college from 1811 to 1815, when he removed to Andover, studying Hebrew and biblical literature. He returned to New Haven in 1824 as professor of theology and sacred literature, a post he retained until his death.
Gibbs was one of the key witnesses in the Amistad trial in 1839-1840. He had been able to locate a translator for the defendants' Mende language by learning to count to ten in that language, and then counting out loud in the harbor of New York City.