Financial terms of the deal weren't disclosed, but a source told ESPN.com's Pierre LeBrun that it is worth $1.5 million in base salary plus potentially more in bonuses.
Zidlicky, 38, had seven goals and 27 assists in an NHL-high 84 regular-season games last season for New Jersey and Detroit. He was scoreless in six playoff games with the Red Wings.
Zidlicky has 85 goals and 316 assists in 783 regular-season games in 11 seasons with Nashville, Minnesota, New Jersey and Detroit. He has a goal and 13 assists in 44 playoff games.
Zidlicky has represented the Czech Republic in three Olympics and six world championships.
The Associated Press contributed to this report.