Chevrier, a 37-year-old Montreal native, was slated to become a free agent Feb. 15.
Chevrier played in all 18 regular-season games last year without making an errant snap while registering nine special-teams tackles. He also played in Calgary's 35-13 loss to Saskatchewan in the West final.
Chevrier has appeared in 157 career games with Calgary.
"Randy has always been a reliable performer at one of the more underrated roles on a football team," head coach/GM John Hufnagel said in a statement. "In addition to his important work on special teams, his work ethic and experience makes him one of our leaders in the locker room."
Chevrier joined the Stampeders in 2005 after two seasons with Edmonton.
"I'm excited to be remaining with the Calgary Stampeders," said Chevrier. "Working with (kicker) Rene Paredes, (punter) Rob Maver, (holder) Bo Levi Mitchell and coach Mark Kilam has been one of the best experiences of my career.
"I think this team has an excellent chance to win it all and I'm looking forward to getting back on the road to the Grey Cup."