The Cardinal, who resigned last week after the allegations came to light, released a statement this afternoon, admitting his sexual conduct had "fallen below the standards expected of a priest, archbishop and cardinal."
Cardinal O'Brien said: "In recent days certain allegations which have been made against me have become public.
"Initially, their anonymous and non-specific nature led me to contest them.
"However, I wish to take this opportunity to admit that there have been times that my sexual conduct has fallen below the standards expected of me as a priest, archbishop and cardinal.
"To those I have offended, I apologise and ask forgiveness.
"To the Catholic Church and people of Scotland, I also apologise.
"I will now spend the rest of my life in retirement. I will play no further part in the public life of the Catholic Church in Scotland."
Cardinal O'Brien is understood to have left Scotland, and he will not attend the Conclave to elect the new Pope.