"My role is to go out there and win," Vick, who is likely to back up Jets starter Geno Smith, told reporters.
"He's a great talent who's won many games, including playoff games," said Jets offensive coordinator Marty Mornhinweg, who was Vick's coordinator for four seasons with the Eagles.
"He's here in a role where he's going to compete and push Geno Smith to become the very best that he can be. Michael will be able to go in and play at a high level and a winning level if called upon."
A four-time Pro Bowl selection, Vick was a standout quarterback for the Atlanta Falcons before spending time in prison on federal gambling and dogfighting charges. He moved to the Eagles in 2009 after being out of the NFL for two seasons.
By terminating their up and down relationships with Sanchez, the Jets freed up $8.3 million in salary cap space.
The fifth overall pick in the 2009 NFL Draft started 62 games with the Jets, posting a 33-29 record while passing for 68 touchdowns and 69 interceptions but spent last season out with a shoulder injury as rookie Smith took the reins.
"We were rookies together and had some early success, becoming the first rookie head coach and quarterback to go to back-to-back championship games," Jets coach Rex Ryan said of Sanchez.
But after leading the Jets to the 2009 and 2010 AFC Championship games, Sanchez's stock dwindled and he had a mammoth 52 turnovers in the 2011 and 2012 seasons.
(Reporting by Ben Everill in Los Angeles, editing by Gene Cherry)