In May, Wilson became the most senior Catholic cleric to be convicted of not disclosing abuse to police.
The abuse was committed by priest James Fletcher in the NSW Hunter Valley in the 1970s.
Wilson insisted he would not step aside until his appeal against his 12-month home detention sentence was complete.
But, amid growing calls for his resignation, Wilson wrote to Pope Francis on July 20 requesting to step aside.
His request was accepted and announced on Monday night.
“I made this decision because I have become increasingly worried at the growing level of hurt that my recent conviction has caused within the community,” Wilson said in a statement.
Prime Minister Malcolm Turnbull welcomed his decision.
“I welcome Philip Wilson’s resignation as Archbishop of Adelaide (on Monday) which belatedly recognises the many calls, including my own, for him to resign,” he said in a statement.
“There is no more important responsibility for community and church leaders than the protection of children.”
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 Fr Fletcher,” he wrote.
“I must end this”.
The appeal is set to continue, the Australian Catholic Bishops Conference said.
The bishops hoped Wilson’s resignation may bring comfort to Fr Fletcher’s victims.
“This decision may bring some comfort to them, despite the ongoing pain they bear,” the ACBC said.
The Adelaide Archdiocese was placed under the care of Bishop Greg O’Kelly following the guilty verdict and he will remain in charge until Wilson’s replacement is appointed by the Pope.
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