Kostitsyn, who's been in the NHL since 2007, had 43 points in 75 games this past season, one year after leading the Predators in goals with 23 and tying for the team lead in points with 50.
Last season the right wing ranked 10th in the NHL in shooting percentage at 17.5 percent.
He's scored 161 points in 307 NHL games with Nashville and Montreal since 2007. He played for Belarus in the 2010 Olympics and the World Championships in May.
Kostitsyn had been scheduled for an arbitration hearing Aug. 2.