Cardinal Keith O'Brien said he was "deeply sorry" for his "sexual conduct".
He was forced to step down two years ago amid allegations he had acted inappropriately towards young priests.
Yesterday Pope Francis accepted the Cardinal's decision to remove himself from the key duties of the role, including, the election of any future Pope and the assistance of the Holy Father in the governance of the Universal Church.
Cardinal O'Brien stepped down as Archbishop of St Andrews and Edinburgh in 2013, issuing an apology at the time, saying "there have been times that my sexual conduct has fallen below the standards expected of me".
After the Pope's decision he issued a new statement: "I wish to repeat the apology which I made to the Catholic Church and the people of Scotland some two years ago now on 3rd March 2013.
"I then said that there have been times that my sexual conduct has fallen below the standards expected of me. For that I am deeply sorry".
"I thank Pope Francis for his fatherly care of me and of those I have offended in any way.
"I will continue to play no part in the public life of the Church in Scotland; and will dedicate the rest of my life in retirement, praying especially for the Archdiocese of Saint Andrews and Edinburgh, for Scotland, and for those I have offended in any way".
Cardinal O'Brien had been a fierce and outspoken critic of gay people, which led many to accuse him of hypocrisy when he accepted claims his 'sexual conduct' involved other men.