The 35-year-old center scored 29 points (13 goals, 16 assists) in 56 regular-season games with the Jets this season, and two points (one goal, one assist) in six Stanley Cup Playoff games.
Stastny could have become an unrestricted free agent Wednesday.
"I feel like at this time of my career, I've seen different places and played for different coaches, different organizations, and it was the best fit for me on the ice and off the ice for my family," Stastny said Tuesday. "We've always enjoyed our time there. I've spoken highly of Winnipeg and I would have never thought that four or five years ago … and that kind of speaks volumes for the organization and volumes from ownership to management to the coaching staff to the players that are there.
"There's a belief that it's a good team that's got a lot of potential and that's got almost all the pieces, and we're close there. And so I think I want to continue that and keep having fun with that."
Stastny said the acquisition of defenseman Brenden Dillon in a trade with the Washington Capitals on Monday reinforced his feeling that the Jets are willing to put the pieces in place for a deep run in the playoffs. Winnipeg traded a second-round pick in the 2022 NHL Draft and in the 2023 NHL Draft to Washington.
"I think he has that sandpaper, that toughness, he's a good player, he can skate, he can make plays," Stastny said. "Everyone thinks they're one or two pieces away, but when you have a goalie like [Connor Hellebuyck] and you have the offensive firepower and some of the dynamic defensemen, you're right there."
Selected by the Colorado Avalanche in the second round (No. 44) of the 2005 NHL Draft, Stastny has scored 755 points (263 goals, 492 assists) in 1,001 regular-season games with the Avalanche, St. Louis Blues, Vegas Golden Knights, and Jets, and 69 points (26 goals, 43 assists) in 103 playoff games.
NHL.com staff writer Tim Campbell contributed to this report
