His latest album Blackstar was released just last Friday, although Bowie had rarely performed or been seen in public in recent months.
Bowie's son Duncan Jones, also known as Zowie Bowie, confirmed the news, writing on Twitter: 'Very sorry and sad to say it's true. I'll be offline for a while. Love to all.'
Other stars paid tribute to the British singer - Sonic Youth's Kim Gordon tweeted: 'So sad to hear of David Bowie dying x'.
Kanye West wrote: 'David Bowie was one of my most important inspirations, so fearless, so creative, he gave us magic for a lifetime.'
Ricky Gervais tweeted, 'I just lost a hero. RIP David Bowie,' while Eddie Izzard wrote: 'Please could every radio station around the globe just play David Bowie music today - I think the world owes him that.'
Cricketer Shane Warne added: 'We can be "Heroes".. You were one of mine. Bowie tunes will be played loud in the Warne house tonight.'
David Cameron also joined the tributes, saying: 'I grew up listening to and watching the pop genius David Bowie. He was a master of re-invention, who kept getting it right. A huge loss.'