Cardinal Sean Brady, the leader of the Catholic Church in Ireland, has apologised and asked for forgiveness as his retirement was confirmed by the Vatican.
The cleric, whose final years at the head of the clergy were dogged by abuse scandals, handed in his resignation on age grounds last month after turning 75, as required under canon law.
Archbishop Eamon Martin will take over as Archbishop of Armagh and Primate of All Ireland - the 116th man to fill the role.
Archbishop Eamon Martin is aged 52 and from the Derry diocese.
He has been lined up as a replacement since his appointment as Coadjutor Archbishop of Armagh in January of last year.
Cardinal Brady was formally installed as Archbishop of Armagh in November 1996, following the retirement of Cardinal Cahal Daly.
His period as Catholic Primate of All Ireland coincided with the church at home and abroad becoming entangled in controversy over the clerical abuse issue.
His actions and inactions, as a priest and later as a cardinal, were part of that saga.
However, it was on his watch that the Catholic Church in Ireland reappraised its responsibilities.
In the last few years, Cardinal Brady faced repeated calls from clerical sex abuse survivors to quit over his involvement in the Fr Brendan Smyth case.
The teacher and canon lawyer swore two victims of the notorious paedophile priest to secrecy during an internal church inquiry in 1975 into the abuse of two children.
Their evidence was never handed over to police, allowing Smyth to continue abusing other youngsters countless times before he was finally jailed in 1994.
The Cardinal insisted his role in the canonical inquiry was as a notetaker.
In a farewell message at mass in St Patrick's Cathedral in Armagh the church leader said he recalled Pope Francis' motto "miserando atque eligendo" which he said "challenges and inspires me with its message of God having mercy and at the same time choosing us, despite our sinfulness".
"It reminds me that I too need to say sorry and to ask forgiveness. And I do so again, now," Cardinal Brady said.
"At the same time, Pope Francis' motto inspires me to trust in the mercy of God and to pray for the strength to do always as Jesus would have me do."
The rapid acceptance of a bishop's resignation within one month is unusual for the Catholic Church, but the former primate's departure has been flagged for some considerable time.
Cardinal Brady led the church in Ireland for more than 17 years during which time a series of investigations exposed shocking levels of clerical abuse.
Last December an investigation by church watchdog the National Board for Safeguarding Children said Cardinal Brady made a "commendable decision to gather and document whatever information was available" about abuse allegations in his own archdiocese on taking up his role as Primate of All Ireland in 1996.
At the time he said he was truly sorry for the suffering of victims.
Although he has also apologised to Smyth's victims, he previously said he would not resign over the affair.
Archbishop Martin paid tribute to the Cardinal and described him as a gentle and humble man who is never fully comfortable in the limelight.
"This is not just my day. It is a day for us to recognise the years of service which you have given to the Church in Armagh and beyond," Archbishop Martin said.
"On behalf of the people, priests and religious of the Archdiocese of Armagh, I want to thank you sincerely for serving us with love and dedication. We appreciate all that you have done for us and we assure you of our continued affection and prayers. We wish you every blessing for a healthy and peaceful retirement."
Archbishop Martin said his appointment was an honour.
Cardinal Brady was the first Catholic Primate to officially meet Rev Ian Paisley.
He was an active promoter of the peace process and he encouraged a greater role for the laity in the Catholic Church.
He will remain working as a priest in the Armagh area and he retains the title of Cardinal.
In a statement, Cardinal Brady said: "I am pleased that Pope Francis has today accepted the resignation which I offered to him on the occasion of my seventy fifth birthday.
"I warmly congratulate Archbishop Eamon Martin who today becomes Archbishop of Armagh, Primate of All Ireland and Coarb Phadraic."
A survivor of clerical child sex abuse who told Pope Francis that Cardinal Brady should stand down has welcomed the Pope's acceptance of the Cardinal's resignation.
Marie Kane was one of six survivors to meet the Pope in the Vatican in June.
She called then for Cardinal Brady to leave office before his resignation had to be offered.
In a message to RTÉ News, Ms Kane said: "Good to hear Seán Brady's letter of resignation (has been) accepted."
Ms Kane was supported in her call by Mark Vincent Healy, the other Irish survivor chosen to meet Pope Francis.