The star, who launched his career with Wham! in the 1980s and continued his success as a solo performer, is said to have “passed away peacefully at home” in Goring, Oxfordshire.
Thames Valley Police say they are treating the death as unexplained but there were no suspicious circumstances.
His former Wham! bandmate Andrew Ridgeley said he was “heartbroken at the loss of my beloved friend”.
Writing on Twitter and referring to Michael as “Yog”, a nickname for “Yours Only George”, he added: “Me, his loved ones, his friends, the world of music, the world at large. 4ever loved. A xx”
In a statement, Michael’s publicist said: “It is with great sadness that we can confirm our beloved son, brother and friend George passed away peacefully at home over the Christmas period.
“The family would ask that their privacy be respected at this difficult and emotional time. There will be no further comment at this stage.”
On Instagram, Sir Elton John posted a photograph of himself with Michael, writing: “I am in deep shock. I have lost a beloved friend – the kindest, most generous soul and a brilliant artist. My heart goes out to his family and all of his fans.”
Thames Valley Police said South Central Ambulance Service attended a property in Goring at 13:42 GMT on Christmas Day.
The force said: “At this stage the death is being treated as unexplained but not suspicious.
“A post-mortem will be undertaken in due course. There will be no further updates from Thames Valley Police until the post-mortem has taken place.”
Treatment for pneumonia
Michael, who was born Georgios Kyriacos Panayiotou in north London, sold more than 100 million albums throughout a career spanning almost four decades.
He first found fame with his schoolfriend Andrew Ridgeley in duo Wham! before going on to release solo albums, including the multi-million selling Faith and follow-up Listen Without Prejudice Vol 1.
It outsold Faith in the UK but led to Michael losing a court case with record label Sony over his frustration over how the album has been marketed.
His talents as a singer, songwriter and music producer made George Michael one of the world’s biggest-selling artists.
Blessed with good looks and a fine singing voice, his stage presence made him a favourite on the live concert circuit as he matured from teen idol to long term stardom.
But there were times when his battle with drugs and encounters with the police made lurid headlines that threatened to eclipse his musical talents.
Excluding his Wham! hits, Michael scored seven number one singles in the UK with songs including Careless Whisper and Faith, and won three Brit Awards and two Grammys.
But as his career faded, Michael faced headlines for the wrong reasons.
In October 2006 he pleaded guilty to driving while unfit through drugs and was banned from driving, and in 2008 he was cautioned for possession of class A drugs, including crack cocaine.
In September 2010, Michael received an eight-week prison sentence following an incident the previous July in which he crashed his Range Rover into a shop in north London. He admitted driving under the influence of drugs and possessing cannabis.