The star, who launched his career with Wham! in the 1980s and had huge success as a solo performer, "passed away peacefully" on Christmas Day in Goring, Oxfordshire, his publicist said.
His manager, Michael Lippman, said he had died of heart failure.
Former Wham! bandmate Andrew Ridgeley said he was "heartbroken at the loss of my beloved friend".
Writing on Twitter and referring to Michael by his family nickname of "Yog", he added: "Me, his loved ones, his friends, the world of music, the world at large. 4ever loved. A xx"
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."
Michael's family announced news of his death in a statement issued through the singer's publicist.
"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," it said.
"The family would ask that their privacy be respected at this difficult and emotional time. There will be no further comment at this stage."
South Central Ambulance Service were called to Michael's property at 13:42 GMT. Thames Valley Police also attended and Michael was confirmed dead at the scene.
They added: "At this stage the death is being treated as unexplained but not suspicious. A post-mortem will be undertaken in due course. "
A small heart wreath and a rose are among the tributes left outside the front door of Michael's home, a detached property by the River Thames.
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 schoolfriend Ridgeley in duo Wham! - reaching number one in the UK singles charts on four occasions. One of the band's most enduring songs Last Christmas, is currently number 16 in the UK singles chart.
The song was originally released in 1984 and is the biggest selling single not to reach number one.
It was kept off the chart's top spot by Band Aid's Do They Know It's Christmas, which actually featured Michael.
Solo albums followed, including the multi-million selling Faith in 1987.
The follow-up Listen Without Prejudice Vol. 1 outsold Faith in the UK but led to Michael losing a court case with record label Sony over his frustration at 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.