The team did not disclose contract details, but a source told ESPN it was a five-year deal worth $50 million, with $28 million in guarantees.
Sanchez, the fifth overall pick at the NFL draft, led Southern California to a 12-1 record last season, including a 38-24 Rose Bowl win over Penn State. He completed 241-of-366 passes for 3,207 yards, 34 touchdowns and 10 interceptions.
With the Jets, he will battle career backup Kellen Clemens for the starting job next season.
"I'm going to go home (to California) for a little bit just to see the family and get all of my stuff out from there and move it here," Sanchez told reporters Tuesday. "I'm still living in a hotel, so I have to figure out my living situation. It's going to be a long season."