A settlement has been agreed by Catholic Archdiocese of Armagh and a man who was one of two teenagers sworn to secrecy about allegations of abuse by Father Brendan Smyth.
Brendan Boland, 50, sued Cardinal Brady, the diocese of Kilmore and Smyth's Norbertine Order.
The High Court was told this morning that the proceedings had been settled and could be struck out.
In a statement following today's proceedings, Mr Boland said he had been abused by Smyth between 1973 and 1975, starting when he was 12 years old.
He brought the matter to the attention of the church authorities, who convened an Ecclesiastical Court.
The then Fr Brady was one of three priests present at the court.
Mr Boland said he was required to swear an oath declaring that he had told the truth and would talk to no one about the interview except "authorised priests".
He said he and his parents were assured Smyth would not be allowed to associate with young boys or girls and there would be no recurrence of the abuse he and others had suffered.
20 years later he discovered that Smyth had gone on to abuse others. Mr Boland said he was devastated by this.
He said the fact that Smyth had been allowed to prey upon and abuse other children subsequent to the assurances having been given was very hard to bear.
He said he felt he had not done enough and felt responsible for the misery of the priest's subsequent victims.
Mr Boland reached a settlement with Gerard Cusack, the Abbot of the Norbertine Order in 2005.
He said that while Cardinal Brady had indicated he would meet him privately, he was disappointed that he had refused, even through his lawyers, to publicly acknowledge and accept the failings of the church in its handling of the circumstances giving rise to this case.
A spokesman for Cardinal Brady said when he was asked to apologise to Mr Boland, he immediately offered to meet him in person to offer that apology.
He said that offer still stood and the Cardinal felt it was the most appropriate way to offer an apology in the circumstances.
The spokesman also said the action this morning was settled by the Archdiocese of Armagh with Mr Boland on the basis that the abuse suffered by Mr Boland occurred in the archdiocese.