Cardinal Brady became the Catholic Primate of all-Ireland in 1996, but the appointment that may define his career was made 21 years earlier.
As a Bishop's secretary in 1975, he was tasked with investigating a complaint of sexual abuse made against a fellow priest, the man who would later be exposed as Ireland's most prolific paedophile, Fr Brendan Smyth.
The manner in which he handled that internal church inquiry has come under intense scrutiny in a BBC 'This World' investigation.
John B Brady was born near Laragh, County Cavan in 1939, one of three children.
He attended St Patrick's College in Cavan before entering the seminary at Maynooth.
On his ordination he returned to Cavan to teach in his old school, and acted as a part-time secretary to the Bishop of Kilmore, the late Bishop Francis McKiernan.
It was in this role that he was asked to deal with the allegations against Brendan Smyth.
A child from Belfast, 14-year-old Brendan Boland, had been taken by Smyth on numerous trips around Ireland.
His deeply-religious parents believed it a privilege to have their son looked so favourably upon by a priest.
In fact Smyth was driving the boy and other children to various guesthouses, where he subjected them to sustained sexual abuse.
When Brendan Boland summoned the courage to tell a local priest about the abuse, that priest immediately drove him to his parents' home.
When his father heard about what his son had endured, he ran into the garden and vomited.
The same priest then drove the boy to tell Smyth's superior, the Bishop of Kilmore.
At his house in Cavan the allegation was levelled, and an internal Church investigation ordered.
Cardinal Brady's part in that Clerical inquiry remained secret until March 2010.
Following two major and damning reports into the handling of clerical abuse in Ireland, it emerged that Ireland's most senior Catholic Priest had himself been involved in a process in which sex abuse was kept from the civil authorities.
At the time Cardinal Brady described his role in the Brendan Smyth investigation as that of a "note-taker".
He and two other priests questioned Brendan Boland at length, and were keen to point out that his parents had accompanied the child to the interview.
What actually happened during that inquiry has now been exposed by reporter Darragh McIntyre, who has uncovered the full extent of Cardinal Brady's involvement.
McIntyre has seen the hand-written notes made and signed by "Father John B Brady" during the course of the interview with Brendan Boland.
Many people will find the nature of the questions put to the child to be shocking.
While it is true that the abused boy's father travelled with him to the interview, he was not allowed inside the room while his son was questioned.
Nor did Brendan Boland feel able to tell his father about what had taken place, as he was sworn to secrecy, upon the Bible, before leaving.
The Cardinal was interviewed about his role in the affair when it came to light in 2010.
When questioned he said, "I think I would resign" if it emerged that anything he had done had allowed the abuse of children to continue.
He claimed that he had "acted effectively to establish the grounds to remove Brendan Smyth".
However, McIntyre's BBC investigation reveals that the teenage victim, Brendan Boland, had also told the then Father Brady and his colleagues, about other children who were being abused by Smyth.
He even furnished the investigating priest and his colleagues with their names and addresses.
Father Brady interviewed one of those boys, who corroborated each of Brendan Boland's claims before being sworn to secrecy.
Father Brady however, failed to inform any parent of the children in the group that they had been abused. Nor were the police told of Smyth's crimes against them.
The result was that Brendan Smyth remained free to abuse another boy identified by Brendan Boland.
His sister and four cousins also remained exposed to Smyth, who continued to attack them over the course of the following 13 years.
Sean Brady may have been selected for the investigation of the matter because he was a Canon lawyer. In the years that followed, his career within the Church went from strength to strength.
In 1980, he was appointed Vice-Rector of the Irish College in Rome, becoming Rector in 1987.
He then returned to Ireland to become the Parish Priest of Castletara, in County Cavan.
In 1995, he was ordained Coadjutor Archbishop of Armagh, and a year later succeeded Cardinal Cahal Daly, to become Archbishop of Armagh, and Primate of all-Ireland.
In 2007, the current Pope Benedict announced that Archbishop Brady was to be made a Cardinal.
There has only been one previous occasion on which a Cardinal has been forced to resign over the issue of clerical sexual abuse.
In 2002, Cardinal Bernard Law was forced to step down as Archbishop of Boston. He was however, subsequently made the archpriest of one of Rome's most important basilicas.
The Catholic Church has said that the "sole purpose of the oath" signed by Brendan Boland in Cardinal Brady's presence was "To give greater force and integrity to the evidence given by Mr Boland against any counter claim by Fr Brendan Smyth".
The Church also points out that in 1975 "no State or Church guidelines for responding to allegations of child abuse existed in Ireland."