Brian Finnegan was accused of not sharing his knowledge of alleged paedophile priests in an attempt to protect himself as well as the church.
The Vatican's press office has announced that the pope has accepted the resignation of the Brisbane auxiliary bishop, upon his reaching the age of retirement.
Mr Finnegan, 77, has been accused of not being open with his knowledge of alleged paedophile priests during his December evidence to the child abuse royal commission's inquiry into the Ballarat diocese.
He was secretary to the bishop of the Ballarat diocese, Ronald Mulkearns, between 1979 and 1985.
During this period, priest Gerald Ridsdale was abusing children in the diocese. He was later convicted.
However Mr Finnegan told the commission that he was not aware of Ridsdale's abuse at the time and had no reason to be concerned about the priest.
The Guardian has reported that the commission heard evidence that Finnegan had been phoned by a mother who was concerned about Ridsdale's interactions with her eldest son.
Documents revealed by the commission also describe the Mortlake parish, where Ridsdale worked as priest in 1981 and 1982, as "a real trouble spot" where there was "drama".
Brian Finnegan's statement that he had not been aware of any abuse were questioned by one of the chair's of the commission.