The legendary entertainer passed away on Sunday, 10 January following an 18-month battle with cancer.
His death was announced on his official Facebook page.
A short post read: "January 10 2016 - David Bowie died peacefully today surrounded by his family after a courageous 18 month battle with cancer. While many of you will share in this loss, we ask that you respect the family's privacy during their time of grief."
Bowie's son Duncan Jones confirmed the news via Twitter, saying: "Very sorry and sad to say it's true. I'll be offline for a while. Love to all."
Thousands of devastated fans have been paying their respects, with more than 22,000 posting on his Facebook page in just one hour.
One fan, @wolfwhistle, wrote on Twitter: "I feel like David Bowie was a beautiful alien we borrowed for a while to make Earth a better place and now he's headed back to his homeland."
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."
Many expressed their shock and disbelief at the news, especially as Bowie has only just released a new album, Blackstar, last Friday and there had been no indication he was seriously ill.
Although he had been recording, his public appearances had been rare in recent years. BBC News says his last live performance was in New York in 2006.