The Rangers will also send a first-round pick in 2015 and a second-round choice in 2014 to the Lightning in exchange for the reigning NHL scoring champ.
Callahan is set to become an unrestricted free agent at the conclusion of the season. TSN Canada also reported that if Callahan re-signs with Tampa Bay, the Rangers would receive a conditional draft pick from the Lightning.
St. Louis, who led the league with 60 points in the shortened 48-game season in 2013, was the leading scorer for the Lightning this season with 29 goals and 32 assists for 61 points in 62 games.
The 38-year-old veteran joined the Lightning as a free agent in July 2000 after spending his first two seasons in Calgary. He helped Tampa Bay to its lone Stanley Cup title in the spring of 2004, when he was also the Hart Trophy winner as the league MVP, and will be reunited with former Lightning teammate Brad Richards in New York.
St. Louis has 369 goals and 604 assists for 973 points in 1,041 career NHL games. He has one year remaining on his contract.
Callahan and the Rangers were trying to work out a new deal. He had spent his entire eight-year career with New York and has 132 goals with 122 assists for 254 points in 450 NHL games.
The 28-year-old Rochester native has 11 goals and 14 assists for 24 points in 45 games this season.
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