The Tampa Bay Lightning signed
The deals come on the heels of the Lightning signing captain Steven Stamkos to a $68 million, eight-year contract.
Hedman will count $7.875 million against the salary cap when the deal begins in the 2017-18 season.
The 6-foot-6, 223-pound Hedman was in the running for the Conn Smythe Trophy as playoff MVP when Tampa Bay lost to the Chicago Blackhawks in the 2015 Stanley Cup Final.
In 473 NHL games, the 25-year-old has 49 goals and 180 assists. Last season he had 10 goals and 37 assists.
Vasilevskiy will count $3.5 million against the cap when his extension kicks in for the 2017-18 season. The contract could mean the end of Ben Bishop's time in Tampa Bay at least by the end of next season when the Las Vegas expansion draft occurs.
General manager Steve Yzerman has said he'll have to trade one of his goalies before June 2017 to avoid one of them being claimed.