The Texans will get a conditional seventh-round pick that can become a sixth based on how much playing time Fitzpatrick gets with the Jets.
The Texans signed Fitzpatrick to a two-year deal worth $7.25 million on March 21, 2014, the same day they traded quarterback Matt Schaub to the Oakland Raiders. The Jets will take on Fitzpatrick's base salary of $3.25 million for the 2015 season.
Fitzpatrick was the odd man out in Houston with the team re-signing Ryan Mallett and agreeing to a deal with free-agent quarterback Brian Hoyer. Both quarterbacks began their careers in New England and spent time there with Texans coach Bill O'Brien.
Fitzpatrick is familiar with Jets offensive coordinator Chan Gailey's system, having played for him when Gailey was the head coach of the Buffalo Bills.
Geno Smith finished last season as the starter in a season that had many downs and few ups. Michael Vick, who replaced Smith briefly as the starter last season, is a free agent.
Fitzpatrick started 12 games for the Texans last season. After the first nine, during which he went 4-5, O'Brien benched him in favor of Mallett, who started two games, playing the second with a torn pectoral muscle. He needed surgery to repair the injury and was placed on injured reserve after that second game.
Fitzpatrick returned for three starts, setting a franchise record with six touchdown passes against the Tennessee Titans in his first of those three. In the third, he suffered a cleanly broken leg and could not finish the season.
Overall, Fitzpatrick threw for 2,483 yards while completing 63.1 percent of his passes with 17 touchdowns and eight interceptions.
Smith has started 29 games in the NFL, in which the Jets have an 11-18 record. New coach Todd Bowles has been reluctant to anoint him as the starter.
ESPN.com Texans reporter Tania Ganguli contributed to this report.