He had been battling the illness for 18 months, and died surrounded by his family.
Speaking on BBC Radio 4, Most Revd Justin Welby said of the musician and actor: "I'm very, very saddened to hear of his death.
"I remember sitting listening to his songs endlessly in the '70s particularly and always really relishing what he was, what he did, the impact he had.
"Extraordinary person."
And Gianfranco Ravasi, the president of the Pontifical Council for Culture, tweeted:
Ground Control to Major Tom Commencing countdown, engines on Check ignition and may God's love be with you (David Bowie)
— Gianfranco Ravasi (@CardRavasi) January 11, 2016
David Bowie famously got crowds to recite the Lord's Prayer at a Freddie Mercury tribute concert in 1992.
The singer released 27 studio albums during a career spanning more than six decades.
He released his final album, Blackstar, just three days ago - on his 69th birthday.
Les Moir, the Artist and Repertoire Director for the Christian record label Integrity Music, told Premier's News Hour David Bowie may have been thinking about life after death right before he died: "Gifts are from God. In Psalm 68 it talks about everyone receiving gifts from God - even those who don't know God.
"So for me he was a challenge, and also an inspiration.
"I don't know if you saw this tribute to Freddie Mercury at Wembley where he gives the Lord Prayer... at the end of his song.
"He was a spiritual man. There's a Lazarus track as well on his new album [Blackstar].
"He would've been thinking about these things, especially having cancer."
Listen to Premier's Antony Bushfield speaking to Les Moir on the News Hour:
