His parentage is uncertain, as are most of the details of his early life. He was said to have graduated from the University of Oxford and to have been a professor of divinity there, but this cannot be confirmed.
He was appointed Bishop of Meath in 1563 when he was in England. He returned to Ireland, was consecrated bishop and made a member of the Privy Council of Ireland. He was always diligent in attendance at Council meetings. He was vigorous in beating off raids on his diocese by Shane O'Neill, the effective ruler of Ulster. He enjoyed the friendship of Sir Henry Sidney, the Lord Deputy of Ireland, who praised his sound judgment, hospitality and blameless private life. His good qualities led Sidney and Adam Loftus, Archbishop of Armagh, to propose Brady as Archbishop of Dublin, after they had lobbied successfully for the recall of Archbishop Hugh Curwen (who became Bishop of Oxford). Shortly after however Brady and Loftus quarrelled, and Loftus blocked Brady's nomination in order to obtain the See of Dublin for himself.
He married Alice, daughter of Robert Weston, Lord Chancellor of Ireland and his first wife Alice Jenyngs. They had numerous children including Luke, their eldest son, and Nicholas, grandfather of his namesake the poet. After Brady's death, his widow remarried Sir Geoffrey Fenton and had further issue, including Catherine, Countess of Cork. The poet Nicholas Brady was the bishop's great-grandson. Maziere Brady, Lord Chancellor of Ireland, was a nineteenth-century descendant of the bishop.
- Fryde, E. B.; Greenway, D. E.; Porter, S.; Roy, I. (1986). Handbook of British Chronology (3rd ed.). Cambridge: Cambridge University Press. pp. 348–350. ISBN 0-521-56350-X.
- “A New History of Ireland Vol XI: Maps, Genealogies, Lists” by Theodore William Moody, F. X. Martin, Francis John Byrne, Art Cosgrove: Oxford, Oxford University Press, 1976 ISBN 0-19-821745-5
- Cotton, Henry (1849). Fasti ecclesiæ hibernicæ: the succession of the prelates and ..., Volume 3 By Henry Cotton. p. 117. Retrieved 2015-11-11.