Born in Massachusetts, Daggett passed most of his professional life in Connecticut, attached to Yale College. His first post after ordination by the Presbyterians was at Smithtown, Long Island, but he moved to New Haven to become professor of divinity at Yale in 1756. Ten years later, he became president of Yale, holding that position until 1777, when he returned to teaching. He was one of the defenders of New Haven in 1779 when the British launched a punitive attack against the city in retaliation for raids by Connecticut privateers. Daggett was captured but was released.