The deal was first reported by Sportsnet‘s Elliotte Friedman.
The 35-year-old centre was slated to become an unrestricted free agent with his three-year, $19.5-million contract signed with the Vegas Golden Knights in 2018 set to come off the books.
Stastny — a 15-year NHL pro, who played in his 1,000th regular season game in May — had 29 points in 56 contests for the Jets, adding two points in six post-season games.
The Quebec City native has recorded 755 points in his NHL career with stints also in Colorado, St. Louis and Vegas.
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