Richard Burke (61), from Fethard, Co Tipperary, had previously stepped down as Archbishop of Benin, in southern Nigeria, after the Vatican investigated a complaint against him of child sexual abuse.
A missionary priest, he also faced being defrocked by the Vatican's Congregation for the Doctrine of the Faith.
In a statement issued yesterday from its Co Wicklow headquarters, the St Patrick's Missionary Society -- known as the Kiltegan Fathers -- revealed that the former archbishop had informed them the reason for his resignation was his failure to observe his oath of celibacy.
"He has apologised to all those whom he has hurt by his actions and has taken full personal responsibility," the statement added.
Archbishop Burke had been accused by Dolores Atwood, a 41-year-old married woman, now living in Canada, of sexually abusing her when she was aged 14.
Affair
She also alleged that she suffered "emotional torture" during a 20-year secret affair.
However, the Kiltegan Fathers said ex-archbishop Burke continued to deny that he was guilty of child sex abuse.
"He is still absolutely insistent that his sexual relationship with Dolores Atwood began when she was over 18 years of age," it said.
The society said that in 2008 it received a complaint from Mrs Atwood, alleging that she had been sexually abused when she was 14 by Archbishop Burke -- then a priest in Warri Diocese, Nigeria -- and that she had an ongoing relationship with him afterwards.
"We expressed the deep sorrow and regret of our society for the suffering she and her family were going through. We also provided counselling for her," the statement said.
"Archbishop Burke was immediately informed. He denied the allegation of child sexual abuse but admitted he had had a sexual relationship with Mrs Atwood.
"He agreed to follow our society's child-protection procedures. After handing over the administration of the Archdiocese of Benin City, he voluntarily withdrew from ministry while we carried out a preliminary investigation."
The society said that Archbishop Burke undertook a psychological assessment and voluntarily entered into a residential therapeutic programme.
"The assessment and therapy indicated that he was in the lowest-possible category of risk of offending against children," it said.
It added that an investigation carried out by the Society's child-protection officer in Nigeria found no evidence to corroborate the allegation of child sexual abuse made by Mrs Atwood.
The society said it was still in touch with Mrs Atwood through a third party and that it had renewed its offer to provide her with counselling.
SIC: II