Weber had 16 points (six goals, 10 assists) in 26 games last season before injuring his foot. In 13 NHL seasons with the Canadiens and Nashville Predators, Weber has 501 points (189 goals, 312 assists) in 867 games. He leads NHL defensemen in goals since the start of the 2005-06 season.
"I think he's really looking forward to coming in here and making an impact," Canadiens forward Brendan Gallagher said. "It's going to be a big boost, but I think we're all excited to watch him play. He's one of the best players in our game for a reason. He has been for a long time. Just as a fan of the game I think you're excited to see him back on the ice."
Weber said he also is looking forward to playing in his first game as Montreal captain. He was named captain Oct. 1, following the trade of Max Pacioretty to the Vegas Golden Knights on Sept. 9.
"It's going to be special," said Weber, who was Nashville Predators captain for six seasons (2010-16). "That was a special moment at the start of the year, but obviously not the same as being able to go out there and help the guys out and be a part of the team in a game situation and feel it through that way."
Weber was paired with David Schlemko at practice Monday, but coach Claude Julien said he wasn't sure if they would remain together Tuesday.
"He's a very welcome addition, not just to the coaching staff but to his teammates," Julien said. "No doubt he'll be an upgrade for us."
To make room on the roster, defenseman Karl Alzner was placed on waivers. Alzner, 30, has one assist in eight games. He was scratched for five games before playing at the Buffalo Sabres on Friday and against the Boston Bruins on Saturday, both 3-2 losses. Alzner is in the second season of a five-year contract he signed July 1, 2017.
"There are a lot of teams right now with injuries on defense," Julien said. "We have a lot of players that are (NHL salary) cap-friendly, who have contracts that are good to take on. We don't want to lose any defensemen. Teams all around the League are looking for more depth on defense. With Karl's contract, we think he's the player we have the least risk of losing. That gives us time to re-evaluate players like (Brett) Kulak, who we only saw for two games. We want to keep Kulak and see what he can do with more than two games.
"It buys us time to make good decisions. Those will come in time. It's tough for Karl, but he was always a team guy. His approach was incredible. It doesn't mean it's irreparable. We might see him again."