Cardinal Brady meets his parishioners in Dundalk on his return from Rome.

Cardinal Brady, a native of Drumcalpin, Laragh, County Cavan attended the local primary school, Caulfield National School. He received a Bachelor of Arts degree in Ancient Classics at St. Patrick's College, Maynooth in 1960. He then earned a Licentiate in Sacred Theology at the Pontifical Lateran University, Rome in 1964. He was ordained in February 1964. He received a Doctorate in Canon Law at the Pontifical Lateran University in 1967.

His first appointment was as professor at his alma mater, St. Patrick's College, Cavan (1967 - 1980). In 1980 he was appointed Vice-Rector of the Irish College, Rome, and in 1987 became Rector of the College, a post he held until 1993 when he returned to Ireland to become Parish Priest of Castletara, Ballyhaise, County Cavan. On 19 February 1995 he was ordained Coadjutor Archbishop of Armagh, and on the retirement of Cahal Cardinal Daly, succeeded as Archbishop of Armagh and Primate of All Ireland on the 1 October 1996. He was installed as Archbishop of Armagh on 3 November 1996.

Following his elevation to the cardinalate he joined Cardinal Daly and Cardinal Connell as one of three living Irish cardinals, a record in Irish history. Senior Vatican figures suggested that the Archbishop's positive contribution to the Northern Ireland peace process will have weighed heavily in Pope Benedict's decision to make him a Cardinal. On his elevation Pope Benedict assigned him the titular church of San Quirico e Giuglietta as a symbol of the new cardinal's role in helping the pontiff to minister to the diocese of Rome

Cardinal Brady, as Archbishop of Armagh and Primate of All Ireland is President of the Irish Episcopal Conference.