Stastny, a 13-year veteran, had 17 goals and 21 assists for the Golden Knights last season. Overall, he has 250 career goals and 726 points in stops with the Colorado Avalanche, St. Louis Blues and Winnipeg, where he played part of the 2017-18 season after being traded.
The 34-year-old has one year remaining on a three-year, $19.5 million contract signed in July 2018.
Dahlstrom, who has 10 assists in his three NHL seasons, has one year remaining on his current deal at $850,000. This past season was his first with the Jets after two seasons with the Chicago Blackhawks.