One of five remaining copies of Hawking's 1965 doctoral thesis from Cambridge University will be part of the auction.
Hawking's items will be featured in a science sale that also includes papers by Isaac Newton, Charles Darwin and Albert Einstein.
Stephen Hawking with the cast of "The Big Bang Theory".
All items will be on display in London from October 30. One is included in the sale, with an estimated price of 10,000 pounds to 15,000 pounds ($13,000 to $19,500).
In addition, the London-based auction house will also put up a copy of "A Brief History of Time", a 1988 best-seller, that is signed with Hawking's thumbprint.
Hawking suffered from amyotrophic lateral sclerosis (ALS), a neurodegenerative disease also known as Lou Gehrig's disease, which is usually fatal within a few years.
By the late 1980s he was at the height of his fame, and given his extensive travels to conferences and public events, as well as the scope of his intellectual explorations of space-time, Christie's said the wheelchair on sale "is arguably both literally and metaphorically the most-travelled wheelchair in history".
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British physicist Stephen Hawking's motorised wheelchair, medals and awards, and a signed copy of his PhD thesis are among a range of items set to go under the hammer in the UK.
As the disease progressed, Hawking began using a wheelchair and communicating with others using a voice-generating computer.
However, he defied all odds, going on to become a towering figure in the world of physics, a bestselling author - particularly with his book A Brief History Of Time - and a father of three and TV celebrity.
A bomber jacket Hawking wore in a 2016 documentary, Stephen Hawking's Favorite Places for the video-on-demand streaming service CuriosityStream, has the lowest starting bid, at £100.
Christie's "On the Shoulders of Giants: Newton, Darwin, Einstein, Hawking" opens for bidding on Halloween, and concludes on November 8.
Lucy Hawking, the late physicist's daughter, told the AP that the auction will give "admirers of [Hawking's] work the chance to acquire a memento of our father's extraordinary life in the shape of a small selection of evocative and fascinating items".