He was educated at Eton and Christ Church, Oxford, and became a fellow of Oriel College.
He married Mary, only surviving daughter and heiress of Denny Muschamp, Esq., of Horsley, Surrey, and his wife Elizabeth Boyle, and, through her, came into a considerable estate.
On 13 July (patent 28 Sept.) 1698, he was created a baronet of Abbeyleix in the Baronetage of Ireland.
Taking holy orders, he was ordained as a priest on 24 June 1700, and, becoming chaplain to James Butler, 2nd Duke of Ormonde, and Archdeacon of Tuam, was by his influence advanced to the bishopric of Killaloe on 12 June 1713.
His only son and heir, John Vesey, was created Baron Knapton in 1750 and was the ancestor to the Viscounts de Vesci and William Vesey-FitzGerald, 2nd Baron FitzGerald and Vesey.