New York went 8-8 last season and missed the playoffs, finishing in second place in the AFC East, four games behind the New England Patriots. Smith, a second-round pick out of West Virginia, started all 16 games, passing for 3,046 yards and 12 touchdowns with 21 interceptions.
The Jets signed veteran quarterback Michael Vick, who spent the past three seasons with Philadelphia, to a one-year deal worth $5 million in May. Vick is expected to compete with Smith for the starting job.
New York opens this season at home against Oakland on September 7.