Financial terms were not announced but local media reported the deal to be worth about $7.5 million a year.
Stamkos, 21, ranked second in the league last season in goals (45) and power-play goals (17) and was fifth in points (91). The center also had eight game-winning goals.
"Steven is extremely important to this franchise and is part of the foundation of our hockey team," Lightning General Manager Steve Yzerman said in a statement.
(Reporting by Gene Cherry in Raleigh, North Carolina)