News of his passing came just hours after he released a short letter to the Church
Addressed to Cardinal Vincent Nichols, to be widely shared, he said: "At this time, the words I pray every night are never far from my thoughts: 'Into your hands, Lord, I commend my spirit'.
"Please tell them that I am at peace and have no fear of what is to come. I have received many blessings in my life, especially from my family and friends.
"I thank God for the many priests, religious and lay faithful who have helped and sustained me in my Episcopal life. Nor should I forget the many Anglican and Free Church colleagues whose friendship I have valued very much.
"Above all, as I now commend myself to the loving mercy of God, I ask them all to pray for me as I remember and pray for them."
Last month it was revealed the 85-year-old had been admitted to hospital after his health took a "defining turn" leading to a number of bishops urging believers to pray for him.
In a statement, current Catholic leader Cardinal Vincent Nichols, said: "As you will know so clearly, for Cardinal Cormac these loving prayers are a source of great strength and comfort as he calmly ponders on all that lies ahead, all in God's good time.
"May the Lord strengthen him in faith and trust and may the prayers of the Church, which he loves so much, comfort and uphold him."
Cardinal Cormac, served as Bishop of Arundel and Brighton from 1977, when he was appointed by Pope Paul VI, until 2000 when he was appointed Archbishop of Westminster by Pope John Paul II.
He handed over the role to Cardinal Vincent Nichols in 2009.