Lightning general manager Julien BriseBois said that signing Vasilevskiy long term was always a high priority.
"Obviously, Andrei is a key member of our NHL team," BriseBois said. "He's arguably the best goaltender in the world and he's just entering his prime now. We had the opportunity to lock him up to a contract that made sense for our organization."
Vasilevskiy tied for the NHL lead in wins (44) with Connor Hellebuyck of the Winnipeg Jets in 2017-18, when he was a Vezina Trophy finalist. He finished third behind Hellebuyck and Pekka Rinne of the Nashville Predators.
The Lightning tied an NHL record with 62 wins last season but were swept by the Columbus Blue Jackets in the Eastern Conference First Round of the Stanley Cup Playoffs.
"The regular season wasn't bad, the Veniza Trophy is good too," Vasilevskiy said. "But the main goal is to win the Stanley Cup, and I won't be happy until I win it. I'm the same guy and I'm going to continue to work hard. This [contract] motivates me to work even harder."
The extension eliminates one of the potential questions the Lightning will deal with this season, when they face uncertainty with the NHL salary cap.
"You're always planning ahead as a general manager," BriseBois said. "You have an idea, a ballpark range, of what that contract is going to be. A cap number of $9.5 million, that's certainly something we can manage going forward. Hopefully, the cap goes up more next offseason than it did this year, but there are certainly no guarantees that will be the case."
Selected by Tampa Bay in the first round (No. 19) of the 2012 NHL Draft, Vasilevskiy is 124-59-15 with a 2.55 GAA and .919 save percentage in his NHL career, and is the Lightning's all-time leader in shutouts (18). He is 15-15 with a 2.83 GAA and .912 save percentage in 33 NHL playoff games.