Hammond is 27-15-6 with a 2.31 goals-against average and .923 save percentage in 56 NHL games (49 starts) with the Colorado Avalanche and Ottawa Senators but has not played in the NHL since the 2017-18 season.
The 34-year-old was 6-2-3 with a 2.44 GAA and .908 save percentage in 11 games with Iowa of the American Hockey League this season.
"It's going to help our goaltending," Canadiens coach Martin St. Louis said Saturday. "'[Cayden Primeau] is going to Laval (of the AHL) and I'll have a little talk with him before he leaves. It's not an easy position to play in the NHL. We needed some reinforcements right now, so we'll meet the new goalie tomorrow."
Hammond was the back up to Sam Montembeault when the Canadiens lost 5-3 to the Buffalo Sabres on Sunday.
In 2014-15, Hammond was 20-1-2 with a 1.79 goals against average and .941 save percentage as a rookie for the Ottawa Senators. With the nickname "The Hamburglar," he helped Ottawa reach the Stanley Cup Playoffs after they were 14 points out of the last spot in the Eastern Conference on Feb. 10.
The Canadiens are without their top two goalies: Carey Price has not played this season because of a knee injury, and Jake Allen is out with a lower-body injury. Primeau (1-7-1, 4.88 GAA, .866 save percentage) and Montembeault (2-10-4, 3.92 GAA, .894 save percentage) have played in their absence.
Montembeault, who made 27 saves Sunday, has played 22 games (15 starts) this season. He missed two games because of an upper-body injury Jan. 22-24.
"Absolutely, all of us are doing our part and this will reduce my workload," Montembeault said. "And with my recent injury, that will allow me to rest it a bit more. [Hammond] is an excellent NHL goalie ... and I'm looking forward to meeting him."
It was the first trade for the Canadiens since Kent Hughes was hired as general manager Jan. 18.
Montreal has allowed the most goals per game in the NHL (3.98) and has been outscored 52-23 in its past 10 games (0-8-2).
The Canadiens lost 5-2 to the Washington Capitals on Thursday in St. Louis' coaching debut. He was hired Wednesday to replace Dominique Ducharme, who was fired.
Baddock, a 26-year-old forward, played one NHL game this season. He scored seven points (three goals, four assists) and had 77 penalty minutes in 33 games with Laval.
NHL.com independent correspondent Sean Farrell contributed to this report
