He was born in Dunsfold, Surrey, England, but his family soon moved to Hampshire, where his father, the Reverend Thomas Warton, became vicar of Basingstoke. There, a few years later, Joseph's younger brother, the more famous Thomas Warton, was born. Their father later became an Oxford professor.
Joseph was educated at Winchester College and at Oriel College, Oxford, and followed his father into the church, becoming curate of Winslade in 1748. In 1755, he returned to his old school to teach, and from 1766 to 1793 was its headmaster, but it was a role in which he did not distinguish himself. His career as a critic was always more illustrious, and he published editions of classical poets such as Vergil as well as English poets including John Dryden. Like his brother, he was a friend of Samuel Johnson.