The President called the Hollywood star a "one of a kind".
His comments came after Susan Schneider, the actor's wife, called her husband one of the world’s “most beloved artists and beautiful human beings”.
Police suspect William’s death was a suicide caused by asphyxiation. Marin County Sheriff's Office added that an investigation into William's death is currently underway.
The star, who appeared in hugely popular films including Mrs Doubtfire and Good Morning Vietnam, was last seen alive at his home, where he lived with Schneider, at around 10pm on Sunday.
Williams shot to fame in the late 1970s as an alien in the US TV comedy series Mork And Mindy, but he won his Oscar as the therapist in the drama Good Will Hunting.
"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," Obama said in a statement, ITV News reported.
In pictures: Robin Williams 1951 - 2014
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"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."
Ms Schneider said in a statement on Monday: “This morning, I 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. On behalf of Robin's family, we are asking for privacy during our time of profound grief. 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."
Her moving comments were echoed by stars who had worked with or knew Williams during his lengthy career.
Steve Martin, who appeared alongside Williams in a 1988 theatre production of Waiting for Godot, said: "I could not be more stunned by the loss of Robin Williams, mensch, great talent, acting partner, genuine soul."
Talk show host Ellen DeGeneres tweeted: "I can't believe the news about Robin Williams. He gave so much to so many people. I'm heartbroken."
Prolific TV and music writer David Wild praised Williams' unpredictable humour.
Ben Stiller, the comedic actor from the generation following Williams', said a tweet was not enough to describe Williams' talents.
30 Seconds to Mars singer and film actor Jared Leto tweeted that Williams was "original" and "brave".
Back to the Future actor Michael J Fox called Williams "kind" and a "genius".
Police are expected to release more information about his death at a press conference scheduled for 7pm British time on Tuesday.
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