The deal is worth $20 million, a source told ESPN.com's Pierre LeBrun.
"He has shown tremendous growth as a player in just more than two seasons in the NHL while also becoming a key member of our team. We look forward to his continued development in a Lightning uniform," Yzerman said in a statement.
Hedman is second on the Lightning in average ice time (22 minutes, 55 seconds a game) and is tied for second on the team for blocked shots with 40.
Hedman, at 6-foot-6, 229 pounds, will turn 21 on Dec. 18. He was the No. 2 overall pick in the 2009 draft.