Lord Habgood was Archbishop of York and second in the Church of England hierarchy for 12 years until 1995.
Dr John Sentamu said: "His towering presence, physical, intellectual, and spiritual, was a gift to all who knew him.
"My prayers are with his family at this time. May he rest in peace, and rise in glory."
He went on: "As a hugely distinguished scientist, theologian and philosopher, Archbishop Habgood's faith in Christ gave him a particular perspective and a persuasive witness both to church and nation for his time. His many books simplified big and complex questions, revealing an incredibly perceptive intellect.
"I'm very glad to have confirmed his grandchildren and dedicated a room in his honour at Bishopthorpe Palace."
Lord Habgood was a key exponent of Christian faith and morals in a secular age.
With his scientific background, he regarded many of the stories on which Christian doctrines are based as being true allegorically rather than literally.
His handling of the situation created by the ordination of women - in which he believed - won him the admiration, even of former critics.
The Revd Canon Dr James Walters, director of the London School of Economics Faith Centre, wrote on Twitter: "Rest in peace John Habgood, former Archbishop of York, a model of intelligent, pastoral Anglicanism.
"Margaret Thatcher once accused him, 'You should be providing moral certainty!'. 'But have you thought', he politely inquired, 'that moral certainty might be a sin?'."