Tampa Bay gets a second-round draft pick in 2012 or 2013, a fourth-round pick in 2013, and center Jon Kalinski. Kalinski played for its AHL team in Adirondack.
Kubina was held out of Tampa Bay's 2-1 win against Washington on Saturday night. He also sat out a game earlier this week because Tampa Bay was shopping him.
Kubina has three goals and 11 points in 52 games. He has 110 goals and 382 points in 953 career games.
He is in the final year of a two-year contract and will become an unrestricted free agent at the end of the season.
"It's tough," Tampa Bay center Steven Stamkos said. "You never want to lose teammates."