The 29-year-old forward was playing this season on a one-year contract he signed on Oct. 9 after attending Rangers training camp on a professional tryout contract.
"It came together pretty quickly, kind of agreed upon yesterday and finalized today," Vesey said. "It's a really good feeling. For me, it's nice to have a little bit of stability. The last few summers have been stressful for me, just not having a contract and waiting around and coming to camp on PTOs.
"It provides some form of validation. I thought I've been playing pretty well this year. It's nice the Rangers want to keep me around. I'm really grateful they brought me in a second time and gave me a second chance again. I just want to keep it going."
Vesey has 12 points (six goals, six assists) in 38 games and ranks fourth among Rangers in short-handed ice time per game (1:29). His ability to play anywhere in the lineup this season has impressed coach Gerard Gallant.
"The last probably 20 games, he's killed a lot of penalities for us, and that's been really important to our group," Gallant said. "He does everything and (he's) getting an opportunity to play with a lot of people. He's worked hard, came to camp and impressed everybody, and continues to do it."
Selected by the Nashville Predators in the third round (No. 66) of the 2012 NHL Draft, Vesey has 147 points (78 goals, 69 assists) in 460 regular-season games with the Rangers, Buffalo Sabres, Toronto Maple Leafs, Vancouver Canucks and New Jersey Devils. He won the 2016 Hobey Baker Award, which is given annually to the best player in NCAA Division I men's hockey, as a senior at Harvard University.
After his senior season at Harvard, Vesey opted not to sign with Nashville, which traded his rights to Buffalo on June 20, 2016. However, he again chose not to sign with the Sabres, making him an unrestricted agent on Aug. 15. Four days later, Vesey signed a two-year, entry-level contract with the Rangers.
Following three seasons with the Rangers, Vesey was traded to the Sabres for a third-round pick in the 2021 NHL Draft on July 1, 2019. He then played for Buffalo, Toronto and Vancouver over the next two seasons before attending training camp with New Jersey on a PTO in 2021-22.
"I think the three years away from here I've learned a lot about myself," Vesey told NHL.com before a 5-3 win against the New York Islanders on Dec. 2. "None of the stops really went as I planned. For whatever reason, I wasn't comfortable, didn't play well. I don't know. One year was a COVID year (2019-20), which was miserable. But I think at this point, this is some of the best hockey I've played. I think I'm more useful to a team now even though I might not score as many goals. I'm really happy with where I am. I think I'm a 200-foot player that can bring a lot of value to a team on a cheaper contract, playing penalty kill and chipping in offensively.
"Deep down I wanted to be here. I kind of flip-flopped. At times I was like, there is opportunity, but at other times I thought they had just been to the (Eastern Conference Final), so it might be a challenge. It was kind of make or break, I went with my gut, and I'm just over the moon with how everything has gone. I had a good camp, parlayed that into a contract and off to a good start."
NHL.com senior writer Dan Rosen and staff writer Jon Lane contributed to this report