The Predators will send a second-round pick in the 2013 NHL Entry Draft to Montreal and will also return the conditional fifth-round pick they received from the Canadiens as part of the February 17 deal that sent defenseman Hal Gill to Nashville.
Kostitsyn, who signed a one-year contract last July to remain with the Canadiens, has 12 goals and 12 assists for 24 points in 53 games this season. He was selected by Montreal with the 10th overall pick in the 2003 NHL Entry Draft and hasn't lived up to those lofty expectations.
The 27-year-old Belarus native has 99 goals and 111 assists for 210 points in 379 games since his debut in the 2005-06 season.
Kostitsyn will join his younger brother Sergei in Nashville. Sergei also began his NHL career with Montreal after being selected in the seventh round of the 2005 draft and was dealt to Nashville in the summer of 2010.