The 26-year-old forward had an NHL career-high 35 points (17 goals, 18 assists) in 81 games with New York last season. He has one season remaining on a two-year contract.
"I'm really excited to be a part of the Sabres and look forward to contributing to the team and seeing what we can do," Vesey said.
"I have a lot of familiarity with Sabres captain] Jack [Eichel], I've known him for quite a long time now, just being from Boston. Last summer and this summer we've been training together so I know Jack well. In terms of other guys, I know [forward] Evan Rodrigues a little bit and obviously we played against each other in college. Through some of my other friends, over the past three years I've gotten to know [forward] Casey Mittelstadt a little bit. The hockey world's a small world so it's nice to have familiarity, though, and that should make it easier for me coming into the locker room."
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Vesey was selected by the Nashville Predators in the third round (No. 66) of the 2012 NHL Draft. But after playing four seasons at Harvard University, where he was a finalist for the Hobey Baker Award as the top player in college hockey in 2015 and 2016, he was traded to the Sabres on June 20, 2016. He did not sign with Buffalo, opted to become a free agent and signed a two-year contract with the Rangers on Aug. 19, 2016.
Buffalo general manager Jason Botterill said that experience three years ago had no bearing on the present.
"From our standpoint, a lot has changed, I think, in the last few years since he'd gone," Botterill said of Vesey. "We're a different organization. We just looked at it as a player that fit a need for us right now. We felt the acquisition price was right, we felt that he brought a different dynamic compared to some of our other wingers, so that's why we stepped up and made the trade.
"We like his size, his speed to get up and down the ice, and I think his game has developed more of a two-way game over the last couple of years. [He was] utilized in that penalty kill last year. But I think the thing that really stands out for us is his ability to score at even strength. I think he's had 16 even-strength goals in each of the last two seasons and has an ability to get to the front of the net, an area that we're trying to improve on for the upcoming season."
Vesey has 90 points (50 goals, 40 assists) in 240 regular-season games and five points (one goal, four assists) in 12 Stanley Cup Playoff games.
"There's definitely been a little bit of evolution in my game," Vesey said. "The past couple of years I've tried to work on my consistency and try to be more impactful on a nightly basis. Last year, something people might not know and something that I'm proud about is that I was able to work on the penalty kill aspect of the game and I saw regular minutes on the PK. I think that was just part of my maturity, being my third year in the League and kind of knowing a little bit more about the defensive zone.
"At the end of the day, I still consider myself a goal-scorer and I think that's my trademark."
NHL.com correspondent Heather Engel contributed to this report
