Marsh was born at Hannington, Wiltshire and educated at Magdalen Hall, Oxford.

In 1679, he was appointed Provost of Trinity College Dublin, where he did much to encourage the study of the Irish language.

Still, after the accession of James II, he was compelled by the turbulent soldiery to flee to England (1689), when he became Vicar of Gresford, Flintshire, and Canon of St. Asaph.

His funeral oration was pronounced by his successor at Dublin, Archbishop King.

A more acerbic account of his character was provided three years prior by Jonathan Swift in his short essay on the "Character of Primate Marsh," which concludes: "No man will be either glad or sorry at his death, except his successor.