The 34-year-old scored a career high 23 goals last season and would have been an unrestricted free agent if the Panthers didn't sign him before Sunday.
"Jozef is a proven playmaker who has fit in very well playing along with our core nucleus of forwards over the past two seasons," said Panthers coach and GM Jacques Martin.
Stumpel has 38 goals, 71 assists and 109 points in 147 games with Florida over the past two seasons.
He has played 905 career NHL games with Boston, Los Angeles and Florida. Stumpel has had at least 50 points in nine of his 13 seasons in the league.