The oft-injured Calvert was limited to 18 games last season by a variety of injuries, including a concussion.
The two-way forward spent his first eight seasons with the Columbus Blue Jackets, who drafted him in 2008. He signed with Colorado in 2018 but finished all three seasons in Denver on the injured list.
Calvert, 31, scored 95 career goals and recorded 203 regular-season points. He had 17 points in 32 career playoff games.
"I've been lucky enough to play the game I love since I was five years old," Calvert said in a statement released through the NHL Players Association. "I never played to make it to the NHL. I played to compete. I played for my teammates. I played for the fans. I played for my family. I played because I loved to battle, and I played to win."
He said that at 18, "I dreamt of becoming an accountant ... and three years later, I was playing in the NHL."
Calvert said he looks forward to "skating on the outdoor rinks" with his sons Kasey and Beau in retirement.
The Avalanche on Thursday also announced the re-signing of forward Kiefer Sherwood, who tallied three assists in 16 games last season.