The singer only released his latest album Blackstar on his birthday on Friday.
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.”
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.”
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.
His last live performance was at a New York charity concert in 2006.
Blackstar, which includes just seven songs, has been well received by critics.
Bowie’s breakthrough came with 1972’s The Rise and Fall of Ziggy Stardust and the Spiders From Mars.
Mark Savage, BBC Music reporter
Today’s news is all the more shocking because David Bowie had recently emerged from suspended animation – revitalised and reinvigorated.
His two last albums, The Next Day and Blackstar, ranked with his best, the former celebrating his past, the latter casting forward to the future. The fact he won’t be there is heartbreaking.
But then Bowie’s entire career has been a vanishing act. The son of a waitress and a nightclub owner, David Jones became David Bowie, who became Ziggy Stardust, who became Aladdin Sane, who became the Thin White Duke. All of them were fictitious. All of them became iconic.
In the 1970s, he was restless, flitting between musical styles and personas, producing Lou Reed and The Stooges, and taking up painting in Berlin. His every move sparked impersonators and inspired musical sub-genres. He was the first post-modern pop star.
He struggled to remain relevant in the 1980s and 90s, but continued to push boundaries with the industrial rock of Outside and the drum and bass influenced Earthling. An enforced hiatus, prompted by an emergency angioplasty, took him out of the spotlight for most of the 2000s before that celebrated, unexpected comeback on his 66th birthday.
That late period of creativity may now be reassessed as the work of a musician who knew his time was running out. But it remains a fitting legacy for a man who subverted and reinvented pop time and time again.
His hits include Let’s Dance, Space Oddity, Starman, Modern Love, Heroes, Under Pressure, Rebel, Rebel and Life on Mars.
He was also well known for creating his flamboyant alter ego Ziggy Stardust.
He also carved out an acting career, including his role as an alien seeking help for his dying planet in Nicolas Roeg’s The Man Who Fell to Earth in 1976.
He did a three-month stint as The Elephant Man on Broadway in the 1980s.
Bowie also starred in Marlene Dietrich’s last film, Just a Gigolo (1978), and played Pontius Pilate in Martin Scorsese’s The Last Temptation of Christ (1988).
Bowie was born David Jones in Brixton, south London, on 8 January in 1947. He changed his name in 1966 after The Monkees’ Davy Jones achieved stardom.
He was in several bands before he signed with Mercury Records, which released his album Man of Words, Man of Music in 1969, which included Space Oddity, his first UK number one.
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