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"
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."