The deal is worth $29 million with $15 million guaranteed, sources told ESPN's Dan Graziano.
Winters, 25, was expected to be one of the most coveted guards on the free-agent market, but he tore his rotator cuff in Week 15 and underwent surgery. He will be sidelined a few months but should be ready for training camp.
It was important for the Jets to retain Winters because he was one of the few players who performed up to expectations last season. He and left guard James Carpenter were the most consistent players on the offensive line, which could be overhauled this offseason.
Winters, a third-round pick in 2013, struggled early in his career at left guard, but he switched to right guard and became the starter midway through the 2015 season, replacing the injured Willie Colon.
The one concern with Winters is his durability; he has yet to start a full season. He underwent major knee surgery in 2014 and missed 10 games. He missed three games this past season, one with a concussion after head-butting Seattle Seahawks defensive lineman Michael Bennett and two due to the rotator-cuff tear.