Meanwhile, one of Scotland's most eminent historians described Cardinal O'Brien's resignation as possibly "the gravest single public crisis since the Reformation" for the Scottish Catholic Church.
There were predictions that the allegations, if true, would shatter its credibility on moral issues and demoralise the faithful.
The Cardinal has said he will be "contesting" the allegations, published in The Observer at the weekend, and was consulting lawyers.
But, in a statement, the normally plain-spoken cleric pointedly made no acknowledgement of the claims.
"For any good I have been able to do, I thank God," he said.
"For any failures, I apologise to all whom I have offended."
Four men – three priests and one former priest – have accused the Cardinal of "inappropriate" behaviour dating back as far as 1980 before he became Archbishop.
Their claims are particularly damaging given his vehement denunciations of homosexuality describing gay marriage as a "grotesque subversion".
The Cardinal was due to retire and had already tendered his resignation to the Pope citing "indifferent health" but no date had been set.
But yesterday, less than 24 hours after it emerged that the Pope was personally overseeing the investigation, he confirmed to the Cardinal that it would now have immediate effect.
The Cardinal said: "The Holy Father has now decided that my resignation will take effect today."
In one of his last acts before stepping down himself, the Pope will now appoint "Apostolic Administrator" to run the archdiocese until a new Archbishop is appointed.
The Cardinal thanked the Pope for his "kindness and courtesy" in the past, adding: "I also ask God's blessing on my brother Cardinals who will soon gather in Rome to elect his successor.
"I will not join them for this Conclave in person. I do not wish media attention in Rome to be focused on me – but rather on Pope Benedict XVI and on his Successor."
Writing for telegraph.co.uk Prof Tom Devine, one of the leading authorities on Scottish history, said: "This is probably the gravest single public crisis to hit the Catholic Church in Scotland since the Reformation and its effects in the short term are incalculable.
"Many of the faithful in Scotland will be stunned by the seismic turn of events and left demoralised."
James MacMillan, the Scottish composer and prominent Catholic said the resignation marked a "terrible day for the Church in Scotland".
Speaking after visiting his home in Edinburgh, the Cardinal's Chaplain, Monsignor Thomas Chambers, said: "[The Church] is over 2,000 years old – it's survived a lot. So we'll come through this together."
But in Rome there was acknowledgement that the decision would overshadow the forthcoming Conclave and uncertainty over the legal status of Cardinal O'Brien's decision to withdraw.
Officials pointedly declined to acknowledge his decision to step aside from the Conclave. Meanwhile support groups for victims of paedophile priests renewed calls for others – including the retired Los Angeles Cardinal Roger Mahony, the former Philadelphia Archbishop Justin Francis Rigali, the Belgian Cardinal Godfried Danneels and Ireland's Sean Brady – to stand aside as well.
Robert Mickens, Rome correspondent for Catholic magazine The Tablet, said: "They don't like to set precedents like that but that is why it is very interesting what has happened with O'Brien.
"We don't know whether it was coordinated, if the Holy See has okayed this or even demanded it.
"He has of course made some erratic statements before.
"All I can say is that it looks very, very strange the timing of this."
Michael Walsh, author of The Cardinals, said: "Other people will be under greater pressure to stay away.
"There has been nothing like this before.
"It is almost as if the fact that the Pope resigned rather than dying in office has created a degree of instability in the Catholic Church."
And the Vatican historian Ambrogio Piazzoni, vice prefect of the Vatican library, said it was unprecedented for a Cardinal to stay away from a Conclave because of a personal scandal.
He said any decision would have to be approved by the full College of Cardinals.
