Wilson, Adelaide's Catholic Archbishop, was under mounting pressure to quit the role and released a statement saying he would step down from his duties on Friday, the Australian Broadcasting Corporation reported.
He is the most senior Catholic bishop in the world to be convicted of the offence.
"It is appropriate that, in the light of some of his Honour's findings, I stand aside from my duties as Archbishop," he said.
"I am now putting in place the necessary administrative arrangements to ensure that the affairs of the Archdiocese are managed responsibly. I therefore intend to step aside as of Friday this week once those arrangements are in place."
But he has stopped short of resigning, saying he would only consider that option if he had to.
Wilson was convicted on Tuesday and is facing possible jail time for not reporting paedophile priest Jim Fletcher to authorities in the 1970s, the Australian Broadcasting Corporation reported.
A magistrate found that Wilson, who was told about the abuse from young victims, dismissed their stories because of his desire to protect the Church's reputation.
Child sexual abuse survivors in Australia have praised the verdict as a milestone in confirming the church's legal accountability for such crimes.
The case is now being treated as a landmark judgment, with lawyers predicting it could trigger prosecutions over other sex abuse cover-ups within the church.
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