Tributes have been led by American President Barack Obama, Prince Charles and Hollywood stars following the death of the 63-year-old, who suffered from a long-term depressive illness.
Williams, who received an Academy Award for his role as a teacher in Good Will Hunting and won legions of fans for comedy roles in movies such as Mrs Doubtfire and Good Morning, Vietnam, was discovered about noon local time on Monday by his concerned employee in San Francisco, sheriff's officials said last night.
Marin County's assistant chief deputy coroner, Keith Boyd, said Williams died by asphyxia.
He said Williams's wife saw the star before she went to bed the evening before and left the house at 10.30am the next day, thinking he was still asleep in another room.
But the actor's personal assistant became concerned when he did not respond to knocks on the door. The assistant went into the room and found Williams dead.
Mr Boyd said Williams had sought treatment for depression, but a full toxicology report would take weeks as the investigation continues.
Williams, who shot to fame as an alien in the US TV comedy Mork And Mindy, was known for his periodic bouts of substance abuse and depression. Last month he announced he was returning to a 12-step treatment programme.
Mr Obama said: "Robin Williams was an airman, a doctor, a genie, a nanny, a president, a professor, a bangarang Peter Pan, and everything in between. But he was one of a kind.
"He made us laugh. He made us cry. He gave his immeasurable talent freely and generously to those who needed it most - from our troops stationed abroad to the marginalised on our own streets.
The Prince of Wales, who met Williams several times, said: "He was a remarkable man, whose wonderful frenetic humour brought a special kind of laughter into people's lives.
"I greatly enjoyed meeting him on several occasions and his irreplaceable contribution to life will be greatly missed by countless people, including myself."
Williams was nominated three times for an Oscar before winning the accolade for his part in Good Will Hunting in 1998.
Andy Dougan, former film critic for The Herald and Evening Times and now a lecturer on film studies at the Royal Conservatoire of Scotland, interviewed him several times. He said: "Robin was a remarkable performer. He was a brilliant comedian but also a very gifted classically trained actor, which people tend to forget. He was also an extremely generous and engaging man.
"Although he was born in Chicago, earlier in his career he once told an interviewer he had been born in Scotland. That stuck for years and he had to keep denying it, but what was true was his great love of Scotland."
Williams's wife Susan Schneider, who was not at home when he died, said she had "lost my husband and my best friend, while the world lost one of its most beloved artists and beautiful human beings. I am utterly heartbroken".
Williams's daughter Zelda, 25, posted an excerpt from a poem on social message site Twitter, which read: "You - you alone will have the stars as no one-else has them ... In one of the stars I shall be living. In one of them I shall be laughing. And so it will be as if all the stars were laughing, when you look at the sky at night ... You - only you - will have stars that can laugh."
She added: "I love you. I miss you. I'll try to keep looking up."
l Anyone seeking help for depression can contact the Samaritans, 24 hours a day, on 08457 909090.