The Chiefs received backup tight end and special-teamer Daniel Brown in the deal. Both players will be free agents after the season.
Duvernay-Tardif, 30, started for the Chiefs in Super Bowl LIV after the 2019 season, but hasn't played a game since that Super Bowl. He was active for the first time this season Monday night against the New York Giants, but saw no action.
Once he gets settled, Duvernay-Tardif could push starting right guard Greg Van Roten, who has struggled at times.
"It's an opportunity to add a Super Bowl champion to the room," Jets general manager Joe Douglas said. "You guys know how I feel about offensive and defensive linemen. If there's an opportunity to improve those rooms, we're going to do it. LDT brings that championship pedigree. A high-character person. Obviously, he's a very smart guy. I can't wait to get him in here and see him compete."
A medical school graduate, Duvernay-Tardif became the first NFL player to opt out last season because of COVID-19 reasons. He opted to continue working at a long-term care facility near his home in Montreal, Quebec.
He returned to the Chiefs this summer for training camp, but injured a hand and missed the preseason. By the time he was healthy, he had been replaced in the lineup by rookie Trey Smith. He was a healthy scratch for the first seven games.
"NYC here we come!" Tardif tweeted, along with a statement thanking the Chiefs organization and fans.
The Jets have been hurt by injuries on the offensive line. In training camp, they lost backup guard Alex Lewis, who decided to retire.
Brown was a core special-teamer for the Jets, but he didn't play much on offense -- only 13 snaps and no receptions.
After weeks of speculation, the Jets didn't trade safety Marcus Maye or wide receiver Jamison Crowder, both on expiring contracts. Douglas was noncommittal on whether he wants to re-sign Maye after the season, a departure from his previous stance. Last spring, he called Maye a priority. They wound up giving him the franchise tag.
Douglas said "there's a lot of meat left on the bone" with regard to the season, meaning he has 10 games before making a decision on Maye's future. He said the organization supports Maye, who faces DUI charges from a February arrest. Douglas called it a "mistake," adding, "We don't condone the action, but we support the man."
He also said he wasn't bothered that Maye hid the arrest from the organization, and the NFL, for seven months. It didn't come to light until it was reported by the media.