Forsberg, a former league MVP who won two Stanley Cups with Colorado and Olympic gold medals in 1994 and 2006, is expected to play during the team's four-game road trip which ends on Saturday in Nashville.
"We're proud to announce that Peter will be back in an Avalanche sweater," Colorado general manager and executive vice president Greg Sherman said in a statement.
"Peter believes he can compete at the NHL level based on how his workouts went. He will provide additional leadership to our club and he will have an impact with this young team."
The 37-year-old Swede, who has 249 goals and 885 points during a 12-season career with the Quebec Nordiques, Avalanche, Philadelphia Flyers and Nashville Predators, played for Modo in the Swedish Elite League last season.
"After testing my abilities with NHL players over the last few weeks, I feel confident that I can play at the NHL level and help this team," said Forsberg, who has been practicing with Colorado since January 22.
"I wanted to see where I was at physically and I am ready for this new challenge."
Forsberg, who represented Sweden at last year's Vancouver Games, joins a Colorado team that has lost four straight games but is only four points off the final playoff spot in the NHL's Western Conference.
(Reporting by Frank Pingue in Toronto; editing by Ed Osmond)