The Jets announced the move on 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.
Morrissey will get paid $8 million in 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.
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.