The young forward had been considering stepping away from hockey due to lingering effects of a skull fracture and concussion sustained during an American Hockey League game in November.
He announced his decision on Monday.
Geoffrion, the grandson of former Canadiens star Bernie Geoffrion and great-grandson of Howie Morenz, told Montreal general manager Marc Bergevin in March that he might retire.
The 6-foot-1 center was skating for Hamilton of the AHL when he sustained a depressed skull fracture from a hit by Syracuse defenseman Jean-Philippe Cote on Nov. 9. Geoffrion underwent surgery the next day.
Geoffrion, a second-round pick in the 2006 draft by Nashville, has eight goals and five assists in 55 career NHL games.