The deal was announced by the team on Wednesday.
The 23-year-old checking winger split last season between the Canadiens and Hamilton of the AHL. In 27 NHL games, he had two goals and three assists with a plus-5 rating in about 9 minutes of ice time per game.
White, a physical forward, is likely to be a regular in the Montreal lineup next season. He has played in 43 NHL games over two seasons after being chosen by the Canadiens with the 66th pick in the 2006 draft.