TSN of Canada is reporting the trade with the Flyers sending a second and fourth round draft pick to the Lightning for the 34-year-old Czech.
Kubina was held out of Thursday's game against San Jose as the team sought to trade him.
The deal is still pending league approval and Kubina would have to waive his no-trade clause.
Over 52 games this season, he has three goals and eight assists along with 59 penalty minutes.
Since breaking into the league with the Lightning during the 1997-98 season, the former seventh round draft pick has totaled 110 goals and 272 assists in 953 games with the Lightning, Thrashers and Maple Leafs.
He was named to the All-Star team in the 2003-04 season and won the Stanley Cup that year with the Lightning.