Dueck, from Vernon, B.C., was chosen by the Canadian Paralympic Committee for having performed "in the moment" throughout the Games, said Team Canada Chef de Mission Ozzie Sawicki.
"Josh embraced this and certainly led by example throughout the alpine events at the Games," Sawicki added.
Dueck, 33, won gold in the men's super combined and silver in the downhill. In all of his events — he raced the giant slalom, slalom and super-G, too — he earned a reputation for pushing the limits and laying it all down on the hill.
"I couldn't be happier right now," Dueck told CBC Sports after learning the news early Sunday. "I was asking myself, 'Do you think the Games get any better?' And I was, like, 'No, they've been pretty much perfect.'
"Then I got the call this morning. It's so cool."
"Skiing's something I love to do, but competing is something I do for Canada, and to have the opportunity to have that exclamation point is [everything I could dream of.]"
Previous closing ceremony flag-bearers include alpine skiers Lauren Woolstencroft and Lana Spreeman, and cross-country skiers Brian McKeever and Colette Bourgonje.
A former freestyle skier, Dueck became a paraplegic in 2004 when he overshot a demonstration jump and broke his back. His downhill medal in Sochi carried special significance because it came on the 10-year anniversary of his life-changing injury.
Dueck has since had an extremely successful career as a sit-skier, recording multiple IPC World Cup podium finishes and Winter X Games medals in the Mono Skier discipline to go along with his Paralympic medals.
Wheelchair curler Sonja Gaudet was Canada's flag-bearer for the opening ceremony.
You can follow the live stream of the closing ceremony at cbc.ca/paralympics beginning at 12:00 p.m. ET (8 p.m. local time).