Stastny, a 34-year-old center, scored 38 points (17 goals, 21 assists) in 71 games with Vegas last season and nine points (three goals, six assists) in 18 postseason games. The Golden Knights lost to the Dallas Stars in five games in the Western Conference Final.
He has one season remaining on a three-year, $19.5 million contract (average annual value $6.5 million) he signed with Vegas on July 1, 2018, and can become an unrestricted free agent after this season.
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Stastny returns to the Jets, who acquired him from the St. Louis Blues on Feb. 26, 2018. He scored 13 points (four goals, nine assists) in 19 regular-season games with the Jets and had 15 points (six goals, nine assists) in 17 Stanley Cup Playoff games to help them advance to the conference final, where they were defeated by the Golden Knights in five games.
"You can't write this stuff up when you're playing the game and thinking about the long-term stuff, but I'm excited to go back to Winnipeg with the guys," Stastny said.
Stastny said he was looking forward to the chance of being reunited on a line with forwards Nikolaj Ehlers and Patrik Laine.
"If that's a possibility, I'm really excited," Stastny said. "Playing with those two guys was like second nature. It's really easy playing with those two guys [who] want the puck; very skilled, dynamic, can score from everywhere. For me, it makes my job easy. Just try to get them the puck as quick as I can."
Selected by the Colorado Avalanche in the second round (No. 44) of the 2005 NHL Draft, Stastny has scored 726 points (250 goals, 476 assists) in 945 games with the Golden Knights, Jets, Blues and Avalanche. He has 67 points (25 goals, 42 assists) in 97 playoff games
"When I talked to him this morning, I told him we tried really hard to make it happen when he was here and to stay here," Jets general manager Kevin Cheveldayoff said. "It was more of a function of the business side of the game… We all understood that then, I told him that obviously we were very excited to have him back with the Jets"
Dahlstrom, a 25-year-old defenseman, had one assist in 15 games with the Jets last season. Selected by the Chicago Blackhawks in the second round (No. 51) of the 2013 NHL Draft, he has 10 assists in 64 regular-season games with the Jets and Blackhawks.
"I think we've got good center depth and that played a part in the decision with Paul," Golden Knights GM Kelly McCrimmon said. "We've got some internal options. Chandler Stephenson is a player that came over and showed the ability to be a good center in the NHL. We have extremely high hopes for Cody Glass as he continues to develop and emerge. Nic Roy was a player that at the start of last season wasn't on our team so there are players right there that their best position is center."