The 23-year-old, who was a restricted free agent, is to earn an average of US$900,000 per season, which is $25,000 less per year than on his previous contract.
The six-foot-three 210-pound de la Rose, mainly a defensive forward, had four goals and eight assists in 55 games for Montreal last season — his first full NHL campaign.
He also helped Sweden win the IIHF World Championship, contributing a goal and an assist in 10 games.
The 2013 second-round draft pick has eight goals and 19 points in 119 career NHL games.
The signing leaves the Canadiens with $12.1 million in unused salary cap space with restricted free agents Phillip Danault and Joel Armia, as well as prospects Kerby Rychel and Michael McCarron, still to be signed.