The 80-year-old, who resigned as Archbishop of St Andrews and Edinburgh in 2013 after admitting sexual misconduct, had recently been injured in a fall.
He died in a Newcastle hospital on Monday.
The Catholic Church has announced the requiem mass will take place at the Church of St Michael in Newcastle on 5 April, with Cardinal Vincent Nichols, Archbishop of Westminster, leading the service.
He will be buried the following day at Mount Vernon Cemetery in Edinburgh in the grave of his mother and father, in accordance with his own wishes.
Cardinal O’Brien resigned from his position in February 2013 after three priests and a former priest alleged improper conduct during the 1980s.
He initially contested the allegations, but later apologised, saying his sexual conduct had “fallen beneath the standards” expected of him.
Announcing his death on Monday, Cardinal O’Brien’s successor as Archbishop of St Andrews and Edinburgh, Archbishop Leo Cushley, said: “In life, Cardinal O’Brien may have divided opinion.
“In death, however, I think all can be united in praying for the repose of his soul, for comfort for his grieving family and that support and solace be given to those whom he offended, hurt and let down. May he rest in peace.”
A statement from the Archdiocese of St Andrews & Edinburgh said: “The requiem mass of Cardinal Keith Patrick O’Brien RIP will take place at the Church of St Michael, Westmoreland Road, Newcastle, on Thursday 5 April at 1pm.
“As requested by the Holy See, the main celebrant and homilist will be His Eminence Cardinal Vincent Nichols, Archbishop of Westminster.
“Donations to SCIAF’s Lenten campaign in lieu of flowers please.”