It follows allegations, which he contests, of inappropriate behaviour towards priests dating from the 1980s.
Pope Benedict XVI has put into effect the resignation, which was tendered some months ago on age grounds.
In a statement this morning, Cardinal O'Brien, 74, said he would not be joining the conclave to choose a successor to Pope Benedict.
He said he did not wish media attention in Rome to be focused on him.
This means Britain will have no representative at the conclave.
Cardinal O'Brien, who is originally from Ballycastle, Co Antrim, stood down from some frontline duties in the Catholic Church in Scotland last year due to his age.
Last week, he said he would be "happy" for priests to be able to marry and that many priests struggle to cope with celibacy.
He said that marriage was not considered when he was studying for the priesthood, but added he would be happy to see it introduced.
Cardinal O'Brien has been an outspoken opponent of the Scottish government's plans to legalise same-sex marriage and was controversially named "bigot of the year" by a gay rights charity last November.