Flames assistant general manager Jay Feaster says the 35-year-old Morrison, who was released from a tryout contract with Vancouver on Sunday, could find himself on Calgary's second line in the short term.
"A skilled guy," Feaster said. "We need a center iceman, we need somebody who is good on faceoffs."
With Daymond Langkow (neck) expected to start the season on long-term injury reserve, and Matt Stajan (shoulder) and Ryan Stone (knee) sidelined indefinitely, the Flames were looking thin down the middle for Thursday's season opener against Edmonton.
Flames forward David Moss (shoulder) and Alex Kotalik (knee) are also out indefinitely.
"Initially, it's a great opportunity to step in and prove you can still produce night in and night out and I'm excited about that," Morrison said on a conference call. "I anticipate coming in and contributing and when the team gets healthier, it's only going to help the cause and help the depth.
"I'm a versatile player who can play center, but if they need me to, I can play the wing. I can play special teams, power play and penalty kill, so I think it's a move that's going to help in a lot of different facets."
Morrison has played 829 regular season games for New Jersey, Vancouver, Dallas, Anaheim and Washington with 187 goals, 360 assists and 424 penalty minutes.
He spent seven seasons with Vancouver and had 12 goals and 30 assists in 74 games last season for the Capitals.
The 5-foot-11, 185-pound forward was a second-round draft pick of the Devils in 1993. He's expected to join the Flames for Tuesday's practice.