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 at the age of 76, is fondly remembered by Paralympians as he opened the 2012 London Paralympics.
Parsons said: “Hawking was a genius of a man, a pioneer and inspiration to us all. While he tested the limits of his imagination, paralympians, you have once again pushed the boundaries of human endeavour."
Team USA topped the medals table, with a total of 36 medals including 13 golds. Canada picked up eight golds among their tally of 28 while France, Germany and Ukraine won seven golds each. Hosts South Korea won one gold – its first at a Winter Paralympic Games - and two bronze.
Towards the end of the ceremony, the Paralympic flag was handed to Chen Jining, the mayor of Beijing, which will host the 2022 Winter Olympics and Paralympics.