Domi has played 222 games with Arizona since his debut with the club in 2015-16 and has produced 36 goals and 135 points.
Last season, the 23-year-old Winnipeg native had nine goals and 36 assists in 82 games. He registered a career-high 52 points with 18 goals in his rookie year.
The 24-year-old Galchenyuk had spent his entire six-year NHL career with the Canadiens after they selected him third overall in the 2012 draft. He scored 108 goals and 255 points in 418 games.