"We can confirm that the funeral of the singer George Michael took place today. Family and close friends gathered for the small, private ceremony to say goodbye to their beloved son, brother and friend," Michael's estate said in a statement.
"George Michael's family would like to thank his fans across the world for their many messages of love and support. We ask that the family's wish for privacy be respected so that they can continue to live their lives privately, away from any media intrusion."
Michael's Wham! band mate Andrew Ridgeley, Pepsi & Shirlie's Pepsi DeMacque, Spandau Ballet bassist Martin Kemp and model Kate Moss were among those who attended the private ceremony, the Mirror reported.
A recent coroner's report found that Michael died of natural causes, with the singer suffering from dilated cardiomyopathy with myocarditis and fatty liver.
"The investigation is being discontinued and there is no need for an inquest or any further enquiries," senior coroner Darren Salter said in a statement. "No further updates will be provided and the family requests the media and public respect their privacy."