According to TSN, the deal is worth $14.7 million with an annual salary-cap hit of $4.9 million.
The 23-year-old Galchenyuk, who was selected by the Canadiens with the third overall pick in the 2012 draft, had 17 goals and 27 assists in 61 games last season. He also provided a spark on the power play, scoring 15 points on that unit.
He missed nearly six weeks to injury this season after banging knees with the Kings' Anze Kopitar in early December.
For his career, Galchenyuk has 89 goals and 115 assists in 336 games.