Acquired from the Minnesota Wild prior to the 2012 NHL Trade Deadline, Zidlicky was a key component in the Devils' run to the Stanley Cup Final with one goal and nine points in 24 postseason games.
Last season, the 36-year-old had four goals and 19 points while playing in all 48 games.
Zidlicky, a sixth-round pick (No. 176) of the New York Rangers in the 2001 NHL Draft, has 66 goals and 325 points in 618 games for the Nashville Predators, Wild and Devils. A power-play specialist, he has 45 career goals with the man-advantage.