Callahan, the Rangers captain, had 16 goals, 15 assists and a plus-9 rating in 45 regular-season games. He had two goals and three assists in 12 Stanley Cup Playoff games.
The 28-year-old wing received the Rangers' Players' Player Award for the third consecutive year, and the Steven McDonald Extra Effort Award for the fourth time.
Hagelin, 24, played all 48 games during the regular season, scoring 10 goals with 14 assists. He had three goals and three assists during the playoffs.
The Rangers defeated the Washigton Capitals in the first round of the playoffs before being eliminated by the Boston Bruins in five games.
Coach John Tortorella -- who during the second round said Hagelin "stinks" on the power play -- was fired Wednesday.