Wilson, who has been diagnosed with Alzheimer's disease, stepped away from his day-to-day work as Archbishop of Adelaide after being convicted.
Pope Francis on Monday accepted the resignation of Australian Archbishop Philip Wilson, the most senior Catholic Church leader to be convicted in a criminal court of concealing sexual abuse, the Vatican said.
Australian Prime Minister Malcolm Turnbull, who this month urged the pope to sack Wilson, said he welcomed the decision to quit, which "belatedly recognises the many calls, including my own, for him to resign".
But Francis hasn't moved on Ezzati's resignation yet, presumably waiting to find the right candidate to take over the leadership of Chile's most important archdiocese.
Philip Wilson has resigned as archbishop of Adelaide.
Archbishop Wilson was found guilty of failing to report the crimes of Fr Jim Fletcher, who was convicted of nine counts of child sexual abuse in 2004.
He had earlier refused to resign, despite his trial at Newcastle Local Court revealing he was told about the abuse in 1976 by two victims - one of them an altar boy who made the revelation at confession.
The archbishop was sentenced July 3 to a 12-month sentence, which will likely be served as house arrest, but said July 4 he planned to appeal the conviction.
The final decision rests with the Vatican but candidates will be considered before a list of possible replacements is sent to Rome, the Apostolic Administrator of the Archdiocese of Adelaide Bishop Greg O'Kelly said on Tuesday.
Wilson's conviction comes amid a host of accusations that the Catholic Church ignored and covered up child abuse in Australia, charges that have also plagued other countries. "I am now 57 years old and continue to struggle with the burden forced upon me".
He was not requested to do so by the Vatican, he said, but he made the decision because he had become "increasingly anxious at the growing level of hurt" his conviction may have caused.
Victim Peter Gogarty said: "Of course".
Wilson said he initially hoped to delay his decision until the appeal was finished. "However, there is just too much pain and distress being caused by my maintaining the office of Archbishop of Adelaide, especially to the victims of Fletcher".