Archbishop Mark Coleridge of Brisbane, president of the Australian bishops' conference, also said that "a number of survivors, prominent Australians and other members of the community have publicly called on Archbishop Wilson to resign".
He hailed Wilson's advocacy for victims in recent years but acknowledged that his refusal to resign after his conviction had reignited memories of the pain the church had inflicted on victims of abuse.
Now, amid rising calls for him to give up his position, he has changed his mind.
Archbishop Wilson, who is suffering from the onset of Alzheimer's disease, told the court he couldn't remember being told about the abuse.
"I have now been informed that His Holiness has accepted my resignation", he wrote.
Adelaide Archbishop Philip Wilson was convicted in May of failing to report to police the repeated abuse of two altar boys by a pedophile priest in the Hunter Valley region north of Sydney during the 1970s.
Australian Prime Minister Malcolm Turnbull, who earlier this month urged the Pontiff to sack Wilson, said he welcomed the decision.More news: England vs India: India's Playing XI for the first Test
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Archbishop Wilson said his decision to resign was because he had become "increasingly anxious at the growing level of hurt" his recent conviction had generated, according to the Archdiocese of Adelaide.
"There is no more important responsibility for community and church leaders than the protection of children", he said. "Philip Edward Wilson", the Vatican said in a statement. Prosecutors, however, uncovered reports of at least four more victims abused by Munoz that were documented by the Santiago archdiocese, including some of his young relatives.
Victim Peter Gogarty said: "Of course".
Fletcher was convicted of nine child sexual abuse charges in 2004, and died in jail in 2006.
He immediately launched an appeal against his conviction after he was handed 12 months detention earlier this month. Magistrate Robert Stone sentenced the 67-year-old on July 3, but delayed a hearing to determine whether he could be given home confinement.
In a short statement released at midday in Rome, the Vatican announced that the Pope had accepted Archbishop Wilson's resignation from the pastoral governance of the archdiocese.