More of Hawking's papers - including "Fundamental Breakdown of Physics in Gravitational Collapse" and "Spectrum of Wormholes" - will be sold as well.
Only five copies of the Ph.D. thesis exist - although a digital copy was made available online for free by Cambridge University Library's Open Access Week past year.
Alongside the wheelchair, the auction will include several Hawking-owned objects, including his medals and awards, his bomber jacket and countless of his original works.
All items will be on display in London from October 30.
Thomas Venning, head of books and manuscripts at Christie's, said Hawking was so despondent over the diagnosis that he "gave up his studies for a time".
At age 22, Hawking was diagnosed with amyotrophic lateral sclerosis, or ALS, just as he was beginning his doctoral work at Cambridge.
Twenty-two lots will be up for auction between October 31 and November 8 in an online Christie's auction known as "On the Shoulders of Giants".
At the time, Hawking was told that he had only 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".
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.
"We are very pleased to have the assistance of Christie's to help us with the important matter of managing our beloved father's archives and his unique and precious collection of personal and professional belongings, chronicling his life and work", said Lucy Hawking in a statement via Christie's.
A Book, written and corrected with handwritten annotation by Stephen Hawking is one of the personal and academic possessions of Stephen Hawking, photo behind, on display at the auction house Christies in London, Friday, Oct. 19, 2018.
Fans can also snag an original production script for The Simpsons episode "Elementary School Musical" (estimated to sell for $2,600-$3,900)-in which Hawking makes his final appearance on the show. This is one of five known copies of Hawking's 117-page thesis, and its estimated value is between $126,000 and $189,000.