The star, who launched his career with Wham! in the 1980s and achieved massive success as a solo performer, “passed away peacefully” 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”
The news was announced in a statement from Michael’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.”