Rookie-free agent quarterback Jake Heaps was waived to make room for Johnson.
The Jets have continued to seek depth at quarterback since Geno Smith’s jaw was broken by a punch from former teammate IK Enemkpali. Ryan Fitzpatrick, acquired in March, will start until Smith returns.
The Jets also signed veteran Matt Flynn to a one-year deal last week, but Flynn is recovering from a hamstring injury he sustained while still a member of the New England Patriots, his previous team, and might not be ready to practice until next week. Fourth-round draft pick Bryce Petty is also on the roster, but not expected to see game action soon.
The Buccaneers selected Johnson in the fifth round of the 2008 NFL draft; he played four seasons with them before signing with the 49ers in 2012.
Smith last appeared in a regular-season game in 2013 with the Bengals. Over 29 career games, he has completed 96 of 177 passes for 1,042 yards, five touchdowns and 10 interceptions. He has also ran 44 times for 274 yards.
- Mike Fiammetta