Australian Archbishop Philip Wilson, the most senior cleric found guilty of concealing child sex abuse in the Roman Catholic Church, has resigned, the Vatican said on Monday.

Wilson, 67, the archbishop of Adelaide, was convicted in May of failing to disclose to police abuse by a priest, Father James Fletcher, after being told about it in 1976 by two victims, one of them an altar boy who told him inside the confessional.

His resignation, which he had earlier refused to submit, comes as a new wave of sexual abuse allegations have hit the highest echelons of the Church around the world, further tarnishing its image and creating the greatest crisis of Francis' pontificate, now in its sixth year.

It came two days after the Vatican announced that the pope had stripped Theodore McCarrick, the former archbishop of Washington, DC, of his rank as cardinal and ordered him to live in seclusion. McCarrick has been accused of sexual abuse of minors and adult seminarians decades ago.

Francis is also fighting an image crisis in Chile, where a growing abuse scandal has enveloped the Church since all 34 of the country's bishops offered to resign.

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'.

'There is no more important responsibility for community and Church leaders than the protection of children,' he said in a statement.

Wilson, who has maintained his innocence, was convicted in May of covering up abuse by Fletcher in the 1970s. Fletcher was found guilty in 2004 of nine counts of child sexual abuse and died in jail in 2006 after a stroke.

Wilson, who is free on bail, is to face court again on August 11, for a ruling on whether he will be imprisoned or allowed to serve his one-year sentence in home detention.

Wilson had earlier refused to resign, saying he would wait until his appeals process for the conviction was finished.

He said in a statement he hoped his decision would be a 'catalyst to heal pain and distress' in the Archdiocese of Adelaide.

'I must end this and therefore have decided that my resignation is the only appropriate step to take in the circumstances,' Wilson said.