Price was assigned to the AHL's Hamilton Bulldogs, as were forwards Maxim Lapierre and Andrei Kostitsyn. Price, 19, was drafted fifth overall by Montreal in 2005 and is seen as the NHL club's goalie of the future. Financial terms of his contract were not disclosed.
The Williams Lake, B.C., native went 30-13-1 with a 2.45 goals-against average, a .917 save percentage and three shutouts in 46 games with the Tri-City Americans, who were knocked out of the WHL playoffs last week.
At the world juniors in Sweden, the six-foot-three, 212-pound Price started all six of Canada's games, posting a 1.14 goals-against average, a .961 save percentage and two shutouts. He was named the tournament's most valuable player and an all-star.
With Price joining the Bulldogs on Tuesday, the Canadiens opted not to send goalie Jaroslav Halak to the AHL club. Halak played most of the season in Hamilton until he was called up in mid-February to replace the injured Cristobal Huet.
Lapierre and Kostitsyn also started the season with Hamilton.
The 21-year-old Lapierre played 46 games with the Canadiens and had six goals and six assists. Kostitsyn, 22, had one goal and 10 assists in 22 games with Montreal.
The Bulldogs end their regular season with four games this week.