The club will immediately begin a search for its next GM.
Tallon spent a decade with the Panthers, who were eliminated by the New York Islanders in Game 4 of their best-of-five qualifying-round series Friday.
The 69-year-old's contract was due to expire after this season.
The Panthers made three postseason appearances during Tallon's tenure but failed to advance beyond the first round; they haven't done so since reaching the Stanley Cup Final in 1996.
Tallon joined Florida in 2010 after serving as GM of the Chicago Blackhawks from 2005-09. While with Chicago, he hired head coach Joel Quenneville, who ultimately led the Blackhawks to three championships. Tallon was eventually demoted to senior advisor and replaced as GM by Stan Bowman before leaving for the Panthers.
Tallon reunited with Quenneville in the Sunshine State last April, hiring him as the Panthers' head coach after Florida missed the playoffs for the sixth time in seven seasons.