Both operations took place Friday, less than a week after New York was eliminated in the second round of the Stanley Cup playoffs by Boston.
Callahan had 16 goals and 15 assists with only 12 penalty minutes in 45 regular-season games. He added two goals and three assists in New York's 12 postseason contests.
Hagelin scored 10 goals and added 14 assists, and posted a plus-10 rating during the regular season, when he was one of four Rangers to play in all 48 games. New York was 14-2-1 when he earned a point and 8-1-1 when he scored a goal.
In the playoffs, Hagelin had three goals and three assists in 12 games.