Published Friday, 15 August 2014
In a statement released on Friday morning, he said that he looked forward to the day it will be accepted.
"Last month I offered my resignation to Pope Francis in accordance with the requirement of Canon Law. I did so in anticipation of my seventy-fifth birthday which I will celebrate tomorrow.
"On 18 January 2013 Pope Benedict XVI acceded to my request for episcopal support and Archbishop Eamon Martin was appointed as Coadjutor Archbishop of Armagh.
"This means that as soon as Pope Francis accepts my resignation Archbishop Eamon will become Archbishop of Armagh and Primate of All Ireland."
He continued: "Archbishop Eamon has been warmly welcomed into the diocese. He has worked tirelessly in getting to know its priests, religious and lay faithful, as well as by becoming involved in every aspect of the life of the Church in Armagh and beyond.
"I look forward to the day when my resignation will be accepted and when Archbishop Eamon will take over as Archbishop, a position for which, I believe, he is excellently prepared."
Editor of the Irish Catholic newspaper Michael Kelly expects Cardinal Brady's resignation to be accepted "in the next number of weeks."
"Every bishop in the world is required to offer to step down at their 75th birthday and Cardinal Brady turns 75 tomorrow (Saturday)," he said.
"In practice, that's rarely accepted. Cardinal Cahal Daly, for example, Seán Brady's predecessor in Armagh, stayed on until he was 79 having submitted his resignation at 75.
"The circumstances here are somewhat different though. Cardinal Brady obviously has been under a lot of pressure. I was talking to some people in the church last night and they were making the point that in some ways he has limped towards this moment.
"I expect the resignation will be accepted probably in the next number of weeks and certainly, I would say, before Christmas."
Cardinal Seán Brady, a native of Co Cavan, has led the church in Ireland for over 15 years.
He was caught up in accusations that he mishandled allegations of child abuse - amid wider cover-ups in the church - after it emerged he interviewed two child victims of paedophile priest Brendan Smyth.
In 2011, Cardinal Brady confirmed he was present at the 1975 meeting where two teenagers abused by Fr Smyth were asked to take a vow of silence.
He apologised for failing to alert the authorities about the serial abuser.
In May 2012, Cardinal Brady said he would not resign over the affair.
Serial sex abuser Smyth was later revealed to be responsible for the rape and assault of hundreds of children in Ireland, Britain and America as the Catholic Church covered up his crimes.
His case rocked the church and the Irish Government - which collapsed in 1994 over delays in granting his extradition to Northern Ireland to face sex abuse charges.
Father Smyth was later jailed and died, aged 70, in August 1997 - one month into his 12-year prison sentence.
© UTV News