The Catholic church in Ireland has been rocked by the abuse scandal
Pope Benedict XVI is expected to accept the resignation of the Bishop of Kildare on Thursday.
Bishop James Moriarty offered to resign in December following publication of the Murphy Report into sexual abuse in the Catholic Church.
Bishop Moriarty, who served as an auxiliary bishop in Dublin from 1991-2002, was barely criticised in the Murphy Report.
He said, however, that he "should have challenged the prevailing culture".
Bishop Moriarty told the Irish Catholic newspaper he did not anticipate resigning when he first read the Murphy Report because he was not directly criticised.
"However, renewal must begin with accepting responsibility for the past," he said.
"Ultimately, I came to the conclusion that we needed a new beginning and that I could play my part in opening the way''.
Bishop Moriarty's resignation is expected to be announced in Rome at 1100 GMT on Thursday.
His departure leaves Bishops Eamonn Walsh and Raymond Field, who resigned on Christmas Eve, awaiting a decision on whether their resignations will be accepted.
The Bishop of Limerick, Dr Donal Murray, resigned in December following criticism of him in the report.
It found that during Dr Murray's time as an auxiliary bishop in Dublin from 1982 to 1996, he was dismissive of complaints about a priest who went on to abuse again.
Galway's Bishop Martin Drennan, who was also named in the Murphy Report though not criticised, has refused to resign, insisting it "would be an injustice".