The 85-year-old died on 1st September after a battle with cancer.
He will be laid to rest within Westminster Cathedral this afternoon following requiem mass, which is expected to be attended by a congregation of more than 1,000 people.
Cardinal Murphy-O'Connor's death prompted tributes from Pope Francis and former prime minister Tony Blair.
Mr Blair, who is not expected to attend the funeral, described him as someone "with a great sense of humour and the sharpest of wits".
Throughout his life, he was an outspoken figure, particularly on the issues of contraception and abortion.
He was installed as the 10th Archbishop of Westminster in March 2000 and the following year he was made a cardinal by Pope John Paul II.
He was ordained bishop of the diocese of Arundel and Brighton in 1977, at which point he became chairman of numerous committees and other Church bodies.
In 2015, he admitted he was deeply ashamed of the way he handled sex abuse allegations concerning priest Michael Hill in the 1980s.
He told the Hay Festival, in south Wales how, as the Bishop of Arundel and Brighton, he allowed the priest to become the chaplain of Gatwick Airport despite Hill confessing to him that he had abused young boys.
He apologised on several occasions to Hill's victims, saying he had made a "grave mistake" and that he had been "naive and ignorant" in his handling of allegations of sex abuse involving Roman Catholic priests.
Cardinal Vincent Nichols, the current Archbishop of Westminster, will say the funeral mass on Wednesday, with the homily due to be given by Archbishop George Stack.