At a spectacular ceremony that featured dancing, music and light shows, the curtain was officially brought down on nine days of sporting action.
"The time has come for me to declare the Pyeongchang 2018 Paralympic Winter Games closed," Parsons said.
Hawking, who died last week aged 76, is fondly remembered by Paralympians as he opened the 2012 London Paralympics.
Parsons paid tribute to the scientist as "a genius of a man, a pioneer and inspiration to us all".
"While Hawking tested the limits of his imagination, Paralympians, you have once again pushed the boundaries of human endeavour," he told the audience.
Towards the end of the ceremony, the Paralympic flag was handed over to the mayor of Beijing -- which will host the 2022 Winter Olympics and Paralympics.
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