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.
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.