The former cardinal resigned last Monday after three priests and a former priest had made allegations of improper behaviour against him dating back to the 80s.
In a statement the cardinal apologised to the Church and the people of Scotland. His statement issued through the Roman Catholic Church in Scotland read:"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."
David Willey, a BBC correspondent in Rome said the news would no doubt affect the mood at the papal conclave at the Vatican. He added "The credibility of the Roman Catholic Church will be further damaged by Cardinal O'Brien's confession of inappropriate sexual behaviour."