A police spokesman said officers went to the stylist's home on Wednesday morning to confirm the death. He said Sassoon had died of natural causes.
Sassoon is regarded as one of the best-known hairdressers of his generation.
He is credited with revolutionising haircuts in the 1960s, and developed a popular line of hair products under his name.
The creator of the "bob" hairstyle, he is best known for his short, geometric cuts, ending the bouffant styles trendy in the 1950s.
One of his best-known clients was Mary Quant, the famous British fashion designer who popularised the mini-skirt. Quant called Sassoon the "Chanel of hair".
In a tribute, fellow British coiffeur and friend Nicky Clarke said he was "hugely significant - the most iconic of hairdressers".
Before Sassoon's arrival on the scene, he said, "people were in rollers, backcombing their hair. What he bought was a different kind of hairdressing.
"It was all about modernism - in some ways he defined the 60s. He helped to put Britain on the map."
Clarke said Sassoon was a "humble person" who "loved his craft", and would be greatly missed.
