Thames Valley Police said the ambulance service had attended a property in Goring in Oxfordshire, where the singer lived, at 1342 GMT on Sunday and a 53-year-old man was confirmed dead at the scene.
“At this stage the death is being treated as unexplained but not suspicious. A post-mortem will be undertaken in due course,” the police said.
Billboard magazine quoted Michael’s manager Michael Lippman as saying the singer had died of heart failure.
Singer Elton John published a picture of himself with Michael on his Instagram account.
“I am in deep shock. I have lost a beloved friend – the kindest, most generous soul and a brilliant artist,” the British star wrote.
Madonna posted a video of herself presenting Michael with an award and wrote: “Farewell my Friend! Another Great Artist leaves us.”
Michael was due to release a documentary in 2017 after a period of living as a virtual recluse in which he hit the headlines for a series of bizarre incidents linked to drugs.
Earlier this month it was also announced that producer and songwriter Naughty Boy, whose real name is Shahid Khan, was working with Michael on a new album for next year.
Michael was best known for his 1980s hits “Last Christmas”, “Freedom”, “Careless Whisper” and “Wake Me Up Before You Go Go” but his career spanned more than three decades.
He won a string of awards including two Grammies and three Brits.
His last album “Symphonica” (2014) rose to number one in the charts.
Many tributes to Michael referred to other music world deaths in 2016, starting with David Bowie in January and including Status Quo guitarist Rick Parfitt who died on Saturday.
“2016 – loss of another talented soul. All our love and sympathy to George Michael’s family,” the band Duran Duran, which were 1980s contemporaries of Wham!, said on their official Twitter account.
Referring to him by his nickname “Yog” (Yours Only George), Wham! co-star Andrew Ridgeley said he was “heartbroken” by Michael’s death.
Canadian musician Bryan Adams tweeted: “I can’t believe it. Such an incredible singer and a lovely human being, far too young to leave us.”
Tributes poured in from outside the music world too.
Football presenter and former England captain Gary Lineker tweeted: “No, not George Michael as well. Another musical great leaves us this year. 2016 can just sod off.”
“Star Trek” actor George Takei referred to some of Michael’s greatest hits in a tweet, writing: “Rest with the glittering stars, George Michael. You’ve found your Freedom, your Faith. It was your Last Christmas, and we shall miss you.”