The Jets announced the move Thursday, one day before the start of training camp.
The deal, which starts in 2020-21 and carries Morrissey through the 2027-28 season, has an average annual value of $6.25 million.
The 24-year-old Morrissey had one year left on a two-year contract with a cap hit of $3.15 million.
"The term excited me," said Morrissey, who's starting his fourth full season in the NHL. "The fact that I get to have that stability, but to be here and playing in Winnipeg, from Day 1, it's what I've always said that I wanted to do."
Morrissey will get paid $8 million in each of the first two years and fourth year of the deal. He receives $5.2 million in the third year, $6.4 million in the fifth year and $4.8 million in each of the last three seasons.
Jets general manager Kevin Cheveldayoff said Morrissey reflects the type of player and person the franchise wants.
"He's done a lot of things both on and off the ice to help our team grow," Cheveldayoff said. "He's mature beyond his years with respect to him as a person.
"Just the way he has progressed and how he earned everything he's gotten on the ice -- the coaches' trust, the coaches' praise, teammates' trust, teammates' praise. Those are things that you earn. In a very difficult sport like this and a very competitive sport, to earn all those people's trust and praise is a big thing."
Morrissey had a career-high 31 points (six goals, 25 assists) in 59 games with the Jets last season.
A first-round pick (13th overall) by the Jets in 2013, Morrissey was third on the team in average ice time last season at 22 minutes 24 seconds.
"We're at a stage here where there's still work to be done and we'll continue to work at that," Cheveldayoff said. "That's pretty much the basis of the most comments I'll give on negotiations, other than we'll continue to work at them and hopefully everything works out sooner rather than later."