The 43-year-old forward had 11 goals and 18 assists in 57 games for the Devils this season. He can become an unrestricted free agent on July 1.
New Jersey will receive Florida's second-round pick in the 2015 NHL Draft and a third-round pick in 2016.
The Panthers are two points behind the Boston Bruins for the second wild card into the Stanley Cup Playoffs from the Eastern Conference. Florida, which has made the playoffs once since 2000 (in 2012), hosts the Chicago Blackhawks on Thursday; Jagr will not play.
"Hopefully [he'll bring] some offense, stability and leadership," Panthers general manager Dale Tallon said. "It's a good opportunity for him to mentor some of our young guys and show them how hard they have to work to get to his level. It brings stability to our young team and gives us an opportunity in the next 20 games to make a good run to make the playoffs."