"The family and close friends of George have been touched beyond words by the incredible outpouring of love for him in the hours and days since his death," the singer's publicist said in a statement.
"Contrary to some reports, there were no suspicious circumstances surrounding his death and from the bottom of our hearts we thank those who, rightly, have chosen to celebrate his life and legacy".
Tearful fans were seen laying tributes on the pavement outside his mansion in Highgate in north London, as well as the house in the village of Goring on the River Thames west of London where he died.
A flag of Cyprus, where Michael's father came from, could also be seen hanging on the railing outside.
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In Goring, one message read: "Your talent was amazing, Your voice was flawless, You gave us all faith, I hope you have found your freedom."
Michael was found dead on Christmas Day by his partner Fadi Fawaz when he arrived to wake him up ahead of a planned festive lunch.
"I went round there to wake him up and he was just gone, lying peacefully in bed," Fawaz was quoted by the Daily Telegraph as saying.
His previous partner Kenny Goss said in a statement: "I'm heartbroken with the news that my dear friend and long-time love George Michael has passed".
"He was an extremely kind and generous man," he said.
Stories about Michael's quiet philanthropy for children and HIV charities have been shared widely since his death, as well as a report of his anonymous 15,000 pound donation to a woman who could not conceive to get IVF treatment.
Michael shot to fame with the band Wham! and sold more than 100 million records in his career, penning a string of famous hits including "Last Christmas", "Faith" and "Wake Me Up Before You Go-Go".