David's son, film director Duncan Jones, confirmed the news and a statement was issued on his social media accounts.
"David Bowie died peacefully today surrounded by his family after a courageous 18-month battle with cancer," it said.
"While many of you will share in this loss, we ask that you respect the family's privacy during their time of grief."
David Bowie's lable only released his latest album Blackstar on his birthday on Friday. The album, which includes just seven songs, has been well received by critics.
Tributes have been paid to Bowie from across the world of entertainment.
Brian Eno, who collaborated with Bowie on his albums Low and Heroes, said: "Words cannot express... rest in peace David Bowie".
Rapper Kanye West said: "David Bowie was one of my most important inspirations, so fearless, so creative, he gave us magic for a lifetime."
Comedian and actor Ricky Gervais, who convinced Bowie to star as himself and ridicule Gervais in an episode of 2006 sitcom Extras, wrote simply: "I just lost a hero. RIP David Bowie."
Comedian and writer Eddie Izzard said: "Very sad to hear about the death of David Bowie but through his music he will live forever."
Bowie collaborator Rick Wakeman wrote on Twitter: "As I'm sure you can imagine I'm gutted hearing of David's passing. He was the biggest influence & encouragement I could ever have wished for."
Will Gompertz, BBC Arts editor
David Bowie was the Picasso of pop. He was an innovative, visionary, restless artist: the ultimate ever-changing postmodernist.
Along with the Beatles, Stones and Elvis Presley, Bowie defined what pop music could and should be. He brought art to the pop party, infusing his music and performances with the avant-garde ideas of Merce Cunningham, John Cage and Andy Warhol.
He turned pop in a new direction in 1972 with the introduction of his alter ego Ziggy Stardust. Glam rock was the starting point, but Ziggy was much more than an eyeliner-wearing maverick: he was a truly theatrical character that at once harked backed to pre-War European theatre while anticipating 1980s androgyny and today's discussions around a transgender spectrum.
He was a great singer, songwriter, performer, actor, producer and collaborator. But beyond all that, at the very heart of the matter, David Bowie was quite simply - quite extraordinarily - cool.
And Prime Minister David Cameron said: "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."
Labour leader Jeremy Corbyn told the BBC Radio 4 Today programme that Bowie was a "great musician, great entertainer", saying he felt "very, very sad" about his death.
"Life On Mars comes flowing back into my mind," he said. "Wonderful song, wonderful guy."