Vick, who signed as an unrestricted free agent, had spent the past five seasons with the Philadelphia Eagles, but was supplanted as the starter due to the rise of Nick Foles.
The Jets made the move to release Sanchez prior to the team having to pay him a $2 million roster bonus, which he was due March 25 if he was still on the roster. Because of the move, the Jets will save $8.3 million against the salary cap.
Sanchez, who becomes a free agent immediately, saw his 2013 season cut short due to surgery on his throwing shoulder.
The 33-year-old Vick played in seven games last season, six of them starts, and completed 77-of-141 passes for 1,215 yards with five touchdowns and three interceptions.
Vick will be reunited with offensive coordinator Marty Mornhinweg, who was at the same position with the Eagles during most of Vick's time in Philadelphia.
The Jets still haven't confirmed Geno Smith as their starter for next season, but bringing in Vick will likely result in fierce competition. Smith started all 16 games as a rookie last year.
More to follow ...