Geoffrion had five points (two goals, three assists) in 35 games with Montreal and the Nashville Predators last season.
The 24-year-old forward, who grew up just outside Nashville, added 21 points (six goals, 15 assists) in 29 American Hockey League games with Hamilton and Milwaukee.
The Canadiens acquired Geoffrion from Nashville for defenceman Hal Gill.
He is the great-grandson of Howie Morenz and the grandson of Bernie (Boom-Boom) Geoffrion, both Hall-of-Fame players with the Canadiens. His father Dan Geoffrion also played for the Habs.
Born in Plantation, Fla., Geoffrion was drafted in the second round, 56th overall by the Predators at the 2006 NHL Entry Draft. He was awarded the Hobey Baker Memorial Award, as the Top U.S. Collegiate Player in 2010.