He was born at Cork, Ireland when his father, John Vesey, was dean of the church there, was educated at Eton and Christ Church, Oxford, and became a fellow of Oriel College. His mother was John's second wife Anne Muschamp. He married Mary, only surviving daughter and heiress of Denny Muschamp, esq., of Horsley, Surrey and his wife Elizabeth Boyle, and, through her coming into a considerable estate. Mary was a cousin on his mother's side. 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 the James Butler, 2nd Duke of Ormonde and Archdeacon of Tuam, was by his influence advanced to the bishopric of Killaloe on 12 June 1713. The following year he became Bishop of Ossory.
He died on 6 Aug. 1730, and was buried in St. Anne's Church, Dublin. 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. Elizabeth Vesey was his daughter. He also had another daughter, Letitia, 1708-1747 who married Ven Charles Meredyth.
- “A New History of Ireland” by Theodore William Moody, F. X. Martin, Francis John Byrne, Art Cosgrove: Oxford, Oxford University Press, 1976 ISBN 0-19-821745-5
- Fryde, E. B.; Greenway, D. E.; Porter, S.; Roy, I. (1986). Handbook of British Chronology (Third Edition, revised ed.). Cambridge: Cambridge University Press. p. 407. ISBN 0-521-56350-X.
- "Fasti Ecclesiae Hibernicae: The succession of the prelates Volumes 1,2 & 4" Cotton, H. Dublin, Hodges & Smith, 1848-1878
- Toby Barnard, ‘Vesey, Sir Thomas, first baronet (1672/3–1730)’, Oxford Dictionary of National Biography, Oxford University Press, 2004 accessed 16 Aug 2015