The 80-year-old resigned as Archbishop of St Andrews and Edinburgh in 2013 and left Scotland after admitting sexual misconduct.
He had been a vehement critic of gay marriage and spoke out against same sex relationships, but later apologised after three priests and one former priest alleged improper conduct in the 1980s.
He died last month in a Newcastle hospital following a fall and his requiem mass was held at the Church of St Michael in the city's West End, close to the Little Sisters of the Poor care home where he had recently lived.
The funeral was led by Cardinal Vincent Nichols, Archbishop of Westminster, and among the 200 mourners were Archbishop Edward Adams, the Papal Nuncio, around 40 priests, and nuns.
Cardinal Nihcols said in his homily: "In recent days, as we all know, the life of Cardinal Keith has been laid bare.
"We all know its lights and its darkness and we need not spend time talking about them even more because he himself gave us the key words to keep in mind.
"In his last will and testament he wrote 'I ask for forgiveness of all I have offended in this life.
"I thank God for the many graces and blessings He has given me especially the Sacrament of Holy Orders'.
"These are the words that guide us as we pray for the repose of his soul, and we also pray for all those he offended and ask God to strengthen them at this time too."
Cardinal Nichols said as well as having failings, there was "great goodness" in Cardinal O'Brien's life, not least his determination to help the poor.
Cardinal O'Brien, who was born in Ballycastle, County Antrim, and grew up in Scotland, trained to be a priest and also taught science at secondary school level.
He will be buried on Friday at Mount Vernon Cemetery in Edinburgh in the grave of his mother and father, in accordance with his own wishes.
Following the Cardinal's death his 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."
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