Beauchemin, 35, signed a three-year contract that TSN reported is worth $13.5 million. He will play the left side on the Avalanche's top defense pairing with Erik Johnson.
Comeau, 29, signed a three-year contract that Sportsnet reported is worth $7.2 million.
"We addressed what we feel are our needs for what we were looking to do today," Avalanche general manager Joe Sakic said. "We're excited to add Beauchemin and Comeau to our group. We've got leadership, we've got toughness, guys that play full 200-foot games.
"The biggest thing is we were looking for somebody to play with [Johnson] for top minutes, play against the other team's top lines. We looked at all the free agents out there, and there's only a handful we knew could play [that role]. Francois did a tremendous job for Anaheim, and I know he's excited to come here and do the same thing."