Quinn, a first-round draft pick of Cleveland in 2007, was cut by Seattle on Saturday. With Mark Sanchez likely sidelined for the opener with a shoulder injury, it appears Smith will get the start against Tampa Bay on Sunday.
The Jets also cut recently signed quarterback Graham Harrell on Monday. The only other quarterback on the team is the inexperienced Matt Simms.
Quinn was once considered the quarterback of the future for the Browns, but has bounced around the league while never living up to those expectations. He has 12 touchdowns and 17 interceptions in six seasons with the Browns, Broncos and Chiefs.