Bourque has no goals in 13 games this season with the Canadiens, who put him on waivers and sent him to their AHL affiliate in Hamilton earlier this month after he went unclaimed.
"I'm happy and looking forward to coming there," Bourque said in a phone interview. "Obviously, I still feel like I have a lot left and I can help the team win."
The 32-year-old wing scored eight goals in 17 playoff games during Montreal's run to the Eastern Conference finals, and Ducks general manager Bob Murray believes Bourque still has NHL goal-scoring ability. He will join the Ducks' roster as soon as he sorts out any immigration issues.
"They're a powerhouse in the Western Conference for quite a while now," Bourque said. "They're built like a playoff team. They have a lot of big forwards, and Bob told me I fit their style of play."
Bourque scored at least 20 goals in three straight seasons for Calgary from 2008 to '11, and he started his NHL career as a steady offensive contributor in Chicago. After his minor league demotion, he was hoping for a trade if he couldn't get another chance to play in Montreal.
"Obviously tough to take after being a regular for 10 years in the NHL. Not something I wanted to go through," Bourque said of his assignment to Hamilton. "Tough days, but maybe the best thing was to get out for a while. Just get a mini-fresh start."
Montreal general manager Marc Bergevin has moved veterans Bourque and Travis Moen this month, shedding more than $5 million from the Canadiens' salary commitments for next season. Bourque will make $2.5 million next year.
Allen has one assist in six games during an injury-slowed season, his third with the Ducks. The stay-at-home defenseman will be an unrestricted free agent next summer, and the Ducks are loaded with blueliners who can do much the same job as Allen, including new free-agent signee Clayton Stoner.
Murray saw the trade as an opportunity to motivate Anaheim's secondary scorers behind Ryan Getzlaf and Corey Perry. Despite the Ducks' position atop the Western Conference at 11-4-5, Ryan Kesler and Matt Beleskey are their only other forwards with more than three goals this season.
"The way things have gone, I'm not particularly happy with the play of our forwards so far," Murray said. "(Bourque) is a big body who can skate, so he'll get an opportunity. ... He's a very streaky scorer. What I do like about him is his size and his skating. I think, at times, we're not moving well enough. I don't know why. We're just not."
Allen also has played for Carolina, Florida and Vancouver, which made him the fourth overall pick in the 1998 draft.