The star, who launched his career with Wham! in the 1980s and had huge success as a solo performer, George Michael, "passed away peacefully" on Christmas Day in Goring, Oxfordshire, his publicist said.
Thames Valley Police say they are treating the death as unexplained but there were no suspicious circumstances.
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"
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 had been called to Michael's property at 13:42 GMT.
Thames Valley Police said its officers 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. There will be no further updates from Thames Valley Police until the post-mortem has taken place."
His manager, Michael Lippman, gave the cause of death as heart failure.
A small heart wreath and a rose are among the tributes that have begun to be left outside the front door of Michael's home, a detached property by the River Thames.