According to the terms of the deal, Clune will make $850,000 in both the 2014-15 and 2015-16 seasons. He was a pending restricted free agent.
Clune, 26, had four goals and five assists in 47 games and was fourth in the NHL in penalty minutes with 113 and led the team with 159 hits last season. He was claimed off waivers by the Predators on January 15.
The Chicago Blackhawks have agreed to terms with forward Kyle Beach on a one-year contract.
Last season with Rockford in the American Hockey League, Beach, 23, had 16 goals and 10 assists and led the team in penalty minutes with 204. In 162 career games with the IceHogs, he has 37 goals and 35 assists.
Beach was the No. 11 overall pick by the Blackhawks in the 2008 NHL Entry Draft.