Graham, who had the ear of presidents and monarchs and reputedly preached to the most people in live sermons in history, died aged 99 at his home in North Carolina on Wednesday.
He spoke to thousands at arenas in the UK during his tours, often referred to as crusades, in the decades following his first visit in 1946.
In 1996, after he stopped travelling because of Parkinson's disease, an estimated 2.5 billion people around the world watched his first "televangelist" show, hosted by Sir Cliff Richard.
And in 2001, Graham was awarded an honorary knighthood by the Queen, whom he had met several times, including in 1984 when he preached at Sandringham Parish Church.
The Most Revd Justin Welby said the church owed Graham an "immeasurable" debt.
He said: "Dr Billy Graham stood as an exemplar to generation upon generation of modern Christians.
"When it comes to a living and lasting influence upon the worldwide church he can have few equals: for he introduced person after person to Jesus Christ.
"There are countless numbers who began their journey of faith because of Dr Graham.
"The debt owed by the global church to him is immeasurable and inexpressible.
"Personally I am profoundly grateful to God for the life and ministry of this good and faithful servant of the gospel; by his example he challenged all Christians to imitate how he lived and what he did.
"He was one who met presidents and preachers, monarchs and musicians, the poor and the rich, the young and the old, face to face.
"Yet now he is face to face with Jesus Christ, his saviour and ours. It is the meeting he has been looking forward to for the whole of his life."
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