Hawking, who was also a cosmologist, astronomer, mathematician and a prolific author, died in March at age 76.
The money raised by the sale of the wheelchair at the auction will go to Stephen Hawking Foundation and the Motor Neuron Disease Association.
Described as "arguably both literally and metaphorically the most-travelled wheelchair in history", the specially-adapted chair had originally been expected to fetch just £15,000.
In total, the auction, which included 52 lots, raised more than 1.8 million pounds (roughly $2.35 million, AU$3.24 million).
Another big hit at the auction was an early motorized wheelchair used by Hawking after he was diagnosed with the neurodegenerative disease amyotrophic lateral sclerosis (ALS) in 1963. Hawking has become one of the most famous theoretical physicists of our time.More news: President Trump says more White House reporters could have credentials revoked
More news: Kane happy to honour Rooney in final England farewell
More news: Sheriff Vet Killed Responding to Calif Shooting - Police Depts Pay Tribute
When Cambridge finally made Hawking's thesis available to download in 2017, it was viewed more than 60,000 times in 24 hours and public interest completely crashed the university's server.
The red wheelchair was used by Prof Hawking during the late 1980s and early 90s; he stopped using it when he could no longer steer it with his hands.
A collection of Hawking's medals and awards fetched almost £300,000 ($392,000) more-again well above the expected price.
The second-highest price of Hawking's collection was achieved by a selection of medals and awards presented throughout his career, which sold for £296,750 ($388,970).
Perhaps more surprising, among some of Hawking's possessions was a script from an episode of "The Simpsons", which raised $8,160 (£6,250).
The physicist's daughter, Lucy, said Christie's had been helping the family & "manage our beloved father's unique and precious collection of personal and professional belongings".