"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," the publicist said in a statement.
Thames Valley Police said the ambulance service had attended his property in Goring in Oxfordshire, at 13:42 GMT on Sunday and confirmed he is dead at the scene. Billboard magazine said 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.
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.
Michael was born Georgios Kyriacos Panayiotou to a Greek Cypriot father and English mother in north London in 1963.
Following years of speculation over his sexuality, Michael came out as gay in 1998 after being arrested for committing a lewd act in the public toilet of a Los Angeles park. It was the first of several incidents that were to overshadow his musical career in his later years.
He notched up police cautions for cannabis and crack cocaine possession and in 2010 was sentenced to eight weeks in jail after crashing his car into a London shop while under the influence of cannabis and prescription medication.
In 2011, he spent several weeks in hospital in Vienna after contracting pneumonia, later saying that he had been close to death.
There were fresh concerns in 2013 when he had to be airlifted to hospital after falling out of his chauffeur-driven Range Rover as it travelled at high speed on a motorway.