He is survived by his wife, Susan Schneider, and three children, Zelda, 25, Zachary, 31, and Cody, 22.
Cobain – the daughter of Kurt Cobain, who took his own life, aged 27, in 1994 – tweeted in response to Zelda’s tribute to her father, a quote from French novel The Little Prince by Antoine de Saint-Exupéry.
"You have such an incredibly beautiful soul," tweeted Cobain. "I love you but you already knew that. Wherever, whenever u need me I'll be there."
@zeldawilliams You have such an incredibly beautiful soul. I love you but you already knew that. Wherever, whenever u need me I'll be thereFrances Bean Cobain (@alka_seltzer666) August 12, 2014
Williams was known for his roles in Good Morning, Vietnam Dead Poets Society, The Fisher King, Good Will Hunting, Mrs Doubtfire, Hook and Jumanji.
Robin Williams: A career in pictures
Robin Williams: A career in pictures
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1980: Robin Williams in the world-famous Mork and Mindy series that launched his career.
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1984: Williams in 'Moscow On The Hudson'. The actor earned his first Golden Globe nomination for his turn as a Russian circus performer in this 1984 hit.
3/30 Robin Williams
1987: Williams in the critically acclaimed 'Good Morning, Vietnam'. Williams ad-libbed all the radio broadcast scenes from this 1987 film about a radio DJ sent to Vietnam to entertain the US troops serving out there.
4/30 Robin Williams
1989: Robin Williams appeared with Robert Sean Leonard and Josh Charles in 'Dead Poets Society' as English teacher John Keating - or the “slightly more daring O Captain, My Captain”.
5/30 Robin Williams
1990: Williams and Robert De Niro in Awakenings, an emotional film that saw Williams portray a British neurologist who administered a drug to catatonic patients that briefly awoke them from decades of catatonia.
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1991: Williams appeared as an adult Peter Pan forced to return to Neverland to rescue his children in 'Hook'. The film received mixed reviews but proved popular at the box office.
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1992: Williams in 'Toys'. The film followed a military general after he inherits a toy factory and decides to produce war toys.
8/30 Robin Williams
1993: Williams appeared in one of his best-loved roles in Mrs Doubtfire, where he played an actor disguising himself as a female housekeeper in order to spend more time with his children.
9/30 Robin Williams
1995: Williams appeared as man released from a board game after being trapped for decades inside it in the blockbuster 'Jumanji'.
10/30 Robin Williams
1996: Williams starred opposite Jennifer Lopez in 'Jack', a film about a young boy who ages four times faster than other children.
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1997: Williams appeared alongside Matt Damon in 'Good Will Hunting', a film that won him an Oscar for his portrayal of psychologist Sean Maguire. As he accepted his award, a touched Williams warned the audience: "Oh man, this might be the one time I’m speechless".
12/30 Robin Williams
1997: The box-office hit Flubber saw Williams take the role of Professor Philip Brainard, who creates the unstoppable green goo Flubber in his bid to produce a new energy source.
13/30 Robin Williams
1998: Williams gave a poignant turn as Dr Hunter 'Patch' Adams, an unqualified doctor who treats patients with laughter in 'Patch Adams' .
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1998: Williams stars alongside Cuba Gooding, Jr in 'What Dreams May Come', a film that follows American physician Chris Nielsen's journey through the afterlife after he is killed in a car crash.
15/30 Robin Williams
1999: Robin Williams, Bob Balaban (left), and Armin Mueller-Stahl star in the movie 'Jakob the Liar' about a Jewish shopkeeper who uses his imagination to engender hope throughout a Polish ghetto in 1944.
16/30 Robin Williams
1999: American Science Fiction drama 'Bicentennial Man' followed an android (Williams) as he experiences emotions and becomes more human
17/30 Robin Williams
2002: Williams took a more sinister role as reclusive crime writer and murderer Walter Finch in 'Insomnia'.
18/30 Robin Williams
2002: Williams undertook an unsettling, psychopathic role in One Hour Photo, where he played a photo lab technician obsessed with a family who frequented the store.
19/30 Robin Williams
2002: Williams starred alongside Danny DeVito in 'Death to Smoochy', a film about a corrupt children's television host disgraced by an FBI sting.
20/30 Robin Williams
2005: Robin Williams stars in 'The Big White', a film about a financially struggling travel agent trying to make a bogus life insurance claim in order to pay for his wife's Tourette treatment.
21/30 Robin Williams
2006: Williams and Ben Stiller star in 'Night at the Museum'. Williams will appear in upcoming film "Night at the Museum: Secret of the Tomb," playing the statue of Teddy Roosevelt who comes to life at night.
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2006: Robin Williams, Jeff Daniels and Cheryl Hines star in roadtrip comedy 'R.V.', which followed the tribulations of a dysfunctional family.
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2006: Williams took the leading role in the political comedy drama 'Man of the Year' about a comedian who decides to run for President and finds himself mistakenly elected.
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2007: Robin Williams and Freddie Highmore in 'August Rush', where Williams played a homeless musician who teaches children living on the streets music and employs them as performers.
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2007: Robin Williams, Mandy Moore and John Krasinski starred in 'License to Wed'. Williams played a reverend who places a couple through a series of tests to see if they should marry in his church. The rom-com was poorly received by critics.
26/30 Robin Williams
2010: Robin Williams and John Travolta star in 'Old Dogs', a comedy that sees two friends and owners of a sports marketing firm struggle to deal with seven-year-old twins placed in their care. The film was nominated for four Golden Raspberry Awards.
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2013: Susan Sarandon, Robert De Niro and Robin Williams star in The Big Wedding
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2013: Williams starred as President Eisenhower in Lee Daniels' 'The Butler'.
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2014: Robin Williams with his Mork and Mindy co-star Pam Dawber in The Crazy Ones series. It was axed after one season.
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2014: Rob Williams stars in 'The Angriest Man in Brooklyn', the story of a bad-tempered man mistakenly told he has 90 minutes to live.
Barack Obama led tributes to the late actor yesterday, describing him as “one of a kind”.
“He made us laugh. He made us cry,” said Obama. “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.”
Other high-profile names to have paid their respects include Steven Spielberg, Steve Martin, Ellen DeGeneres, Ben Stiller and Jared Leto.
His children have also published a statement, describing their “immeasurable loss” of their “father and best friend”.
“He was always warm, even in his darkest moments,” said Zelda.
“While I'll never, ever understand how he could be loved so deeply and not find it in his heart to stay, there's minor comfort in knowing our grief and loss, in some small way, is shared with millions.”