Versteeg had 21 goals and 25 assists with Toronto and Philadelphia last season. The right winger had seven goals in 27 games with the Flyers, who had acquired him at the trade deadline.
Versteeg spent his first three NHL seasons with Chicago and was a member of the Blackhawks' Stanley Cup-winning team in 2010.
To get Versteeg, the Panthers gave up a conditional second-round pick in the 2012 or 2013 NHL Entry Draft, along with a third-round pick in 2012 previously acquired from San Jose.
Versteeg will join a Florida team that has signed free agents Ed Jovanovski, Jose Theodore, Scott Upshall and Marcel Goc.