A three-year NHL veteran, Domi had played 222 games with Arizona since debuting with the club in 2015-16, amassing 36 goals and 135 points along the way.
Last season, the 23-year-old Winnipeg native ranked third on the Coyotes with 45 points (9g - 36a) in 82 games. He registered a career-high 52 points (18g - 34a) during his rookie year.
Internationally, Domi won gold at the 2015 IIHF World Junior Hockey Championship. He also claimed a gold medal at the 2016 IIHF World Hockey Championship as well.
The two-time OHL champion, who has averaged 0.61 points per game over the course of his NHL career, was a first-round pick of the Coyotes, 12th overall in 2013.
For his part, Galchenyuk had spent his entire six-year NHL career to date with the Canadiens, amassing 108 goals and 255 points in 418 games.
The 24-year-old Milwaukee, WI native was the third-overall selection of the Canadiens back in 2012.