It was revealed last month that Cardinal Murphy-O'Connor had been admitted to hospital after his health took a "defining turn".
Cardinal Cormac, whose parents were from Cork, served as the tenth Archbishop of Westminster from 2000 until his retirement in 2009.
Cardinal Vincent Nichols of Westminster issued a statement saying his predecessor "died peacefully this afternoon, surrounded by his family and friends".
Cardinal Murphy-O'Connor was once described by The Tablet, a Catholic weekly, as "everyone's favorite bishop: human, genial, collaborative, imposing".
Speaking to the BBC, Cardinal Nichols said that his lasting memory of Cardinal Murphy-O'Connor would be his "laughter and of his joy in life, music, and sport, and in company and in having a good chat". "Pray, too, for his family, and those many friends and colleagues from the diocese and far beyond who mourn his loss". He was a bishop in 1985 when he moved Michael Hill into the chaplaincy at Gatwick Airport.
Cardinal Cormac had argued Catholic adoption agencies should be exempt from new laws, but later welcomed Mr Blair into the Catholic Church when the former prime minister converted after leaving office.
He became the first member of the Catholic hierarchy to preach to an English monarch in more than 500 years when he gave a sermon at Queen Elizabeth II's Sandringham estate in 2002. With the death of Cardinal Murphy-O'Connor there are now 222 living cardinals, of whom 120 are eligible to vote in a papal conclave.
Archbishop of Canterbury Justin Welby, the spiritual leader of the world's Anglicans, said people saw in Murphy-O'Connor "something of Christ".
"His humility, sense and holiness made him a church leader of enormous impact", Archbishop Welby said.
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