Speaking outside Armagh Cathedral on Tuesday morning, the defiant 70-year-old Primate told UTV that, after much consideration, he felt he was best placed to lead the Catholic Church forward.
"It certainly wasn't an easy decision," he told UTV.
"I have listened to a lot of people, reflected as I said I would. I listened to survivors, to priests, to religious people up and down the length of this diocese and I have decided to continue in my present role, to play my part in this diocese," he said.
The primate also vowed to lead the church's efforts to improve child protection measures.
"I want to maintain the momentum towards better child safeguarding and not alone that, also the momentum towards renewal of the faith, which is essential here and a big challenge."
Cardinal Brady has resisted calls to quit since it was revealed earlier this year that he was present at a meeting 35 years ago, where two teenagers abused by paedophile priest Father Brendan Smyth were asked to take a vow of silence.
He did not report the case to civil authorities at the time.
On St Patrick's Day, Cardinal Brady had told mass-goers that he would take a period of time to reflect on his future in the church and spent weeks meeting survivors of abuse publicly and privately.
When asked by UTV what he would say to reassure victims, Dr Brady said:
"I am deeply sorry that they were abused by anybody but especially if it happened by priests or religious.
"I'm sorry if my decision yesterday has upset them. I want to only do what is healing, which I think is the first thing, the programme of healing of those people."
Cardinal Brady has asked the Pope for extra help to push through measures to deal with sex scandals. It is thought that will mean that a Bishop will be appointed to work alongside him.
Anger
Mass goers leaving St Patrick's Cathedral on Tuesday morning expressed their support for the Cardinal, but abuse survivors have voiced their anger at his decision to stay on.
"What about all the victims? What about all Catholics who were abused in all the parishes and children's homes right across the north of Ireland?" Sam Adair, who was one of the victims of Fr Smyth, asked.
"It brings shame on all Catholics here. Any Catholics that I speak to want this whole issue of child sex abuse resolved", he added.
Campaigner Margaret McGuckin, who was physically abused in the Catholic Church-run Nazareth House in south Belfast, said she was astonished by the decision.
"The older generation is more forgiving but not this generation," she said.
"They need to see what has been done by actions. For him to stay in his position I don't think the Catholic Church will recover from that.
"If it was any other workplace in society the thing to do would be to step down or be fired," she added.
Cardinal Brady indicated that he would not quit on Monday night, following the announcement of an all-island audit into how the Church handles abuse allegations.
The Primate said he had asked for his own diocese to be inspected by Vatican officials.
The Cardinal went on to praise the work of the National Board for Safeguarding Children in the Catholic Church, which will run the review.
He also confirmed the diocese of Armagh would appoint a full-time director of child safeguarding to handle all future suspicions and allegations of abuse and report directly to civil authorities.
He said diocesan staff have been asked to fully participate in the soon to be created Independent Safeguarding Authority in Northern Ireland.
It will allow the sharing of soft information on clergy, and the Cardinal urged a similar system be set up in the Republic, and to allow cross-border sharing of information.