Christie's, a London-based auctioneer, handled the sale, which was first announced back in October.
A bidder also spent more than US$760,000 - more than double the expectation - on Prof Hawking's signed 1965 PhD thesis, Properties of Expanding Universes, about the origins of time and space.
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A red leather wheelchair that Hawking used from the late 1980s to the mid-1990s, driving himself using a joystick, sold for £296,750 while an early edition of his bestselling book "A Brief History of Time" marked with a thumbprint, fetched £68,750. It was sold for $760,000. Only five copies of the thesis exist in the world, although digital copies have been made available to the public for free.
The most expensive item in Hawking's collection was a copy of his Ph.D. dissertation on the expansion of the universe. The physicist spent most of his life steadily losing control over his muscles because of amyotrophic lateral sclerosis, or Lou Gehrig's disease.
Image: This Simpsons script - an episode that featured Professor Hawking - sold for £6,250.
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When the document was made available online a year ago by Cambridge University, where Hawking spent his career, it was so popular that it crashed the website.
Other items in the collection also sold for two thousand pounds each.
One of his most famous works was his landmark book a "A Brief History of Time", which sold more than 10 million copies. His various medals and awards raised a total of £296,750 or about $390,000.
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Altogether, the items auctioned, which also included possessions of Isaac Newton, Charles Darwin and Albert Einstein, were sold for more than US$2.3 million. Hawking's daughter, Lucy, oversaw the auction. The scientist died 14 March 2018 at his home in Cambridge. He was 76 years old.