The left wing was acquired from the Carolina Hurricanes on Wednesday for two draft picks,
the second major trade in two weeks by Jets general manager Kevin Cheveldayoff.
Tlusty arrived in Winnipeg shortly before the morning skate and likely will skate on the second line with center Mark Scheifele and Stafford.
"[The whirlwind] was a little wild, but it is part of it and it's kind of fun too," said Tlusty, who had 13 goals and 10 assists with Carolina this season. "It's great to be here. When I heard the news I was really excited. Leaving [Carolina] was hard but I'm really excited to be here and part of the Jets."