Medals, awards, scientific papers and the script for one of Prof Hawking's appearances on The Simpsons will also be going under the hammer as part of the sale, entitled On the Shoulders of Giants.
It will be auctioned by Christie's online alongside a range of his other valued possessions and the proceeds will be donated to the Stephen Hawking Foundation and the Motor Neurone Disease Association.
Hawking's well-known 1988 book "A Brief History of Time" signed with his thumbprint is also available to buyers.
Auction house Christie's will expose on auction a total of 22 items, among them - one of his wheelchairs and doctoral thesis.
The cosmic visionary was diagnosed with motor neuron disease at 22 and was given just a few years to live.
Mr Venning said the wheelchair became a symbol not just of disability but of Professor Hawking's "puckish sense of humour".
Hawking died in March at age 76. He communicated through a voice-generating computer and moved in a series of high-tech wheelchairs.
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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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.
This particular chair is the last one used by Hawking while he still had control of his hands and before needing more sophisticated technology.
Autograph manuscript, notes and extracts from the "Turba philosophorum",[Cambridge, 1670s]. In 1977, for example, Prince Charles reportedly got his toes crushed beneath Hawking's wheelchair, and the scientist joked that he regretfully did not get a chance to run over Prime Minister Margaret Thatcher's feet as well.
Daughter Lucy Hawking has noted that, through the auction, fans of the scientist will get the chance to become owners of the relics, reminding about the unusual life of a theoretical physicist.
Hawking will be in good scientific company at the auction.
Hawking's items will be featured in a science sale that also includes papers by Isaac Newton, Charles Darwin and Albert Einstein.
Christie's hopes to fetch between £10,000 and £15,000 for it during the sale which opens on October 31.