Stastny said he liked what he saw from the Golden Knights in their first NHL season.
"I think they play such a high-paced game, aggressive, and everyone is involved in the game, not just one line," he said. "It's all four lines. When you teach that philosophy, you create a lot of chances, you create a lot of turnovers, which gets you the puck. I like playing (on) teams that are aggressive and play on their toes and teams that aren't afraid to make mistakes. That was big.
"Just looking at the kind of players that they have, a lot of speed, a lot of goal-scorers, and that to me, I feel I fit well with that."
Vegas general manager George McPhee said he had coveted Stastny for some time.
"He's a really talented, skilled guy," McPhee said. "He's a playmaker and you always want playmakers. It's hard for goal-scorers to score if they don't have playmakers. He does that. He's a real good person, good solid pro. We do like having centers. You can move centers around the lineup, you can have centers on the wing, you can't get wingers to play center."
Stastny improves the center depth of the Golden Knights, who were fifth in the NHL in scoring last season (3.27 goals per game). William Karlsson, who's a restricted free agent, was center on the top line in 2017-18. Already signed for this season are Cody Eakin, Erik Haula, Pierre-Edouard Bellemare and Ryan Carpenter.
Stastny played almost exclusively with wings Patrik Laine and Nikolaj Ehlers for Winnipeg.