The Mrs Doubtfire star was found dead at his home in California, having recently grappling with severe depression.
His family spoke of their heartbreak and paid tribute to a husband and father.
Williams’ wife Susan Schneider 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. As he is remembered, it is our hope the focus will not be on Robin’s death, but on the countless moments of joy and laughter he gave to millions.”
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His daughter Zelda Williams, 25, posted an excerpt from French poet and aviator Antoine de Saint-Exupery’s The Little Prince on 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.”
Mara Buxbaum, Williams’ press representative, said: “Robin Williams passed away this morning. He has been battling severe depression of late.
“This is a tragic and sudden loss. The family respectfully asks for their privacy as they grieve during this very difficult time.”
Police said the death of the Good Morning, Vietnam actor was a suspected suicide.
A Marin County Sheriff’s Office statement said: “At this time, the Sheriff’s Office Coroner Division suspects the death to be a suicide due to asphyxia, but a comprehensive investigation must be completed before a final determination is made.”
It added that an investigation into the “cause, manner, and circumstances of the death is currently under way”.
A forensic examination is expected to take place today, with toxicology tests later.
Police were called to Williams’ home in the town of Tiburon, California, at around 11.55am local time yesterday (7.55pm BST) after receiving a call that a man was unconscious and not breathing.
Police and firefighters arrived on the scene five minutes later, but the actor was pronounced dead at 12.02pm.
Williams was last seen alive at his home, where he lived with Ms Schneider, at around 10pm on Sunday, the sheriff’s office added.
The Oscar winner, who had battled addiction for decades, checked himself back into rehab last month.
But his representative said at the time that he had not fallen off the wagon and was ensuring that he focused on his commitment to stay sober.
Williams shot to fame in the late 1970s as an alien in the US TV comedy series Mork & Mindy.
But it was his role as an irreverent DJ with the US Armed Services Radio station in Good Morning, Vietnam in 1987 which won him huge acclaim.
His roles ranged from serious and dramatic in movies such as Dead Poets Society and Good Will Hunting, to comedy in Mrs Doubtfire and Mork & Mindy.
He was Oscar nominated three times before winning an Academy Award for his performance as a psychologist in Good Will Hunting in 1998.
US president Barack Obama led tributes to the star, saying: “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 arrived in our lives as an alien - but he ended up touching every element of the human spirit. 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 Obama family offers our condolences to Robin’s family, his friends, and everyone who found their voice and their verse thanks to Robin Williams.”
The Prince of Wales, who met Williams several times, also paid tribute, saying: “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.”
Steven Spielberg, who directed Williams in the 1991 film Hook, called the actor “a lightning storm of comic genius” saying “our laughter was the thunder that sustained him”.
“He was a pal and I can’t believe he’s gone,” he added.
Steve Martin, who appeared alongside Williams in a 1988 theatre production of Waiting For Godot, said that he was “stunned by the loss of Robin Williams, mensch, great talent, acting partner, genuine soul”.
Night At The Museum co-star Ben Stiller praised Williams’ “kindness and generosity” adding “And he could not help but be funny all the time.
“He would do something as long as it would keep you laughing. He made many, many film crews laugh out loud before the audiences ever saw it. He made such a big impact on the world.”
Friend Henry Winkler, who played The Fonz in Happy Days, where Williams’ Mork made his debut, told CNN: “I am speechless that this great, great artist is no longer on the earth. It is unimaginable that this is the reality today.”
Garry Marshall, creator of Mork & Mindy, said that he would “never forget the day I met him and he stood on his head in my office chair and pretended to drink a glass of water using his finger like a straw....He could make everybody happy but himself”.
Stephen Fry said that the star had “a brain wired like no other” and was “so, so kind”, Rory Bremner called the actor a “Catherine wheel of comic energy.. his imagination was like electricity” while comedian Billy Connolly hailed Williams as his “true friend and my hero”.
Police are expected to release more information about Williams’ death at a press conference scheduled for 7pm British time today.
The actor returned to TV last year in the show The Crazy Ones, alongside Sarah Michelle Gellar, but the series was cancelled after one series.
There were reports in recent months that Williams could be reprising his Mrs Doubtfire role, as a divorced man who disguises himself as an elderly, female nanny to see his children, for a sequel.
Less than three months ago he appeared on screen alongside Mila Kunis in The Angriest Man In Brooklyn, playing a terminally-ill man, in the final movie featuring Williams to be released before his tragic death.