Archbishop of Adelaide Philip Wilson was convicted on Tuesday in the Newcastle Local Court, north of Sydney, of concealing the sexual abuse of two altar boys by a paedophile priest in the 1970s.
The 67-year-old who has Alzheimer's disease was released on bail and faces a prison term of up to two years when he is sentenced next month.
Wilson said he would stand aside on Friday after administrative arrangements were made to manage his archdiocese. He said he was still discussing the magistrate's decision with his lawyers.
"While I do so, it is appropriate that, in the light of some of his Honor's findings, I stand aside from my duties as archbishop," Wilson said in a statement.
"If at any point in time it becomes necessary or appropriate for me to take more formal steps, including by resigning as archbishop, then I will do so," he added. He has not said whether he is considering an appeal.
Wilson was once Australia's highest-ranking archbishop as president of the Australian Catholic Bishops Conference.
Before Wilson announced he would step down, Frank Brennan, an Australian Jesuit priest, human rights lawyer and academic, said the move was inevitable.
"There's no doubt that Archbishop Wilson in recent years ... has been one of the good guys. He has been one of the bishops in the Catholic Church who have been trying to clean things up," Mr Brennan said.
"But this relates to when he was a young priest. Even someone like him who later got it back in those years was so confined by our culture that it would seem there was no disclosure," he added.
An Australian inquiry into child abuse recommended in December that the Catholic Church lift its demand of celibacy from clergy and that priests be prosecuted for failing to report evidence of paedophilia heard in the confessional.
An altar boy testified at Wilson's trial that in the mid-1970s the then-priest had refused to believe the boy's allegations of abuse made in the confessional.
Australia's longest-running royal commission - which is the country's highest form of inquiry - had been investigating since 2012 how the Catholic Church and other institutions responded to sexual abuse of children in Australia over 90 years.
The report heard testimony from more than 8,000 survivors of child sex abuse. Of those who were abused in religious institutions, 62% were Catholics.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.