Hayes avoided a salary arbitration hearing and signed a one-year contract with the Rangers on July 30, 2018. He can become an unrestricted free agent July 1.
[RELATED: 2018-19 NHL Trade Tracker | Hayes wore Jets jersey as child]
The 26-year-old center has 42 points (14 goals, 28 assists) in 51 games this season.
"I actually woke up pretty early this morning and tuned into NHL Network, and the TV was saying I got traded, but I hadn't really heard from anyone at my end," Hayes said. "My agent called me and told me he thinks it might be Winnipeg, but I never really knew.
"Then I started getting texts from people saying, 'Congrats on the move.' Finally, I got the call from my GM and he told me about everything. And then I talked to the GM of the Jets and some people that work for the Jets and got my flight situated. It's been a pretty hectic day. I'm actually picking up my gear right now, and then will probably head to the airport."
The Rangers also received a first-round pick in the 2019 NHL Draft and a conditional fourth-round pick in the 2022 NHL Draft. Should the draft lottery render the 2019 first-round selection a top-three pick, the Rangers will instead receive a 2020 first-round selection. If the Jets win the Stanley Cup this season, New York gets their 2022 fourth-round pick.
Hayes was held out of the Rangers' past two games leading up to the 2019 NHL Trade Deadline.
"It hasn't been too bad," Hayes said of the speculation about his future. "I knew I was probably going to be traded. I tried not to think about it, but it definitely played a little bit of a role. It was pretty emotional saying goodbye to some of the guys, but I'm excited to get going here and to finally get back to playing for a Stanley Cup and playing for a good team."
Winnipeg (37-21-4) enters play Monday first in the Central Division, one point ahead of the Nashville Predators.
"Kevin is a good fit for us in many, many ways," Jets general manager Kevin Cheveldayoff said. "He's someone, I think everyone talks about, obviously, his size and his offensive abilities, but I really think what's really going to shine through here is his defensive abilities as well.
"Penalty-killer, responsible -- he's someone, over the course of his career, has grown his game from just being a pure offensive player in high school and in college and grown his game to a really mature professional game."
Selected by the Chicago Blackhawks in the first round (No. 24) of the 2010 NHL Draft, Hayes signed with the Rangers as a free agent Aug. 20, 2014. He has 216 points (87 goals, 129 assists) in 361 regular-season NHL games and 10 points (two goals, eight assists) in 34 Stanley Cup Playoff games.
"It's tough," Hayes said. "This is really all I've known since I've been in the NHL, with the Rangers. I was lucky enough to play here for five years. I have nothing but respect for this organization and nothing but great memories here. It's tough to leave a city like this and a team like this and the friendships that you build with some people, it's definitely tough. But I'm excited to get going here."
Jets forward Blake Wheeler reached out to Hayes to welcome him after the trade was made official. Hayes said he thinks the transition to Winnipeg will be smooth.
"I'm really close with Rick Nash and he went through the same situation last year, so he's helped me out a little bit," said Hayes, who will wear No. 12. "It's definitely tough going to a new team but, I mean, it's going to be an easy situation, I think. Everyone knows someone. One of my friends definitely knows someone on the Jets and they're going to reach out and it's going to be an easy transition. It's definitely a crazy situation but I'm excited to get it going.
"There's definitely a little bit of a difference between the Eastern and Western Conference. I've obviously been in the Eastern Conference my whole career. But they're a big, heavy team and they got some elite players, so I'm hoping to step in and it'll be an easy transition. We play the (Minnesota) Wild tomorrow, so it should be a pretty good test right away."
Hayes credited former Rangers coach Alain Vigneault and current coach David Quinn for helping him become a well-rounded player.
"I'm definitely a big center that can skate pretty well and try to make guys around him better," Hayes said. "I'm definitely a pass-first-type player, so hopefully I can build some chemistry with some guys right away."
Lemieux, a 22-year-old forward, has 11 points (nine goals, two assists) in 44 games this season. Selected by the Buffalo Sabres in the second round (No. 31) of the 2014 NHL Draft, he has 12 points (10 goals, two assists) in 53 NHL games, all with the Jets, who acquired him in a trade with Buffalo on Feb. 11, 2015.
The Jets also acquired defenseman Nathan Beaulieu in a trade from the Buffalo Sabres for a sixth-round pick in 2019, forward Matt Hendricks in a trade from the Minnesota Wild for a seventh-round pick in the 2020 NHL Draft, center Par Lindholm in a trade from the Toronto Maple Leafs for forward Nic Petan, and defenseman Bogdan Kiselevich in a trade from the Florida Panthers for a seventh-round pick in the 2021 NHL Draft.
The Rangers (27-26-9) are nine points behind the Carolina Hurricanes for the second wild card into the playoffs from the Eastern Conference.
New York traded forward Mats Zuccarello, who could become a UFA on July 1, to the Dallas Stars on Saturday for two future draft picks.
NHL.com correspondent Scott Billeck contributed to this report