Belknap was born in Boston, Massachusetts, the son of a tanner. His uncle was Mather Byles, one of New England's intellectual leaders. Belknap was baptized by the historian Thomas Prince, another leading figure of 18th-century New England. He was educated at the Boston Latin School and Harvard College, where he graduated in 1762. In 1764 he moved to Portsmouth, New Hampshire, where he "kept the school" and studied theology with Samuel Haven (Harvard College class of 1749). In 1767 he began his ministry in Dover, New Hampshire, where he would spend twenty years at the Congregational Church.