Johnson was released Tuesday by the Cincinnati Bengals after losing the No. 2 job to AJ McCarron. The Jets worked out Johnson on Thursday as coach Todd Bowles said the team was keeping its options open.
"We are just kicking the tires around in case somebody else gets hurt," Bowles said before the team signed Johnson later in the evening. "Just taking a look at quarterbacks."
With Geno Smith (broken jaw) expected to miss the first four games, Ryan Fitzpatrick is the starter. The Jets, looking for an emergency quarterback with experience, signed Matt Flynn last week, but they gave him no guarantees other than a $60,000 signing bonus.
Flynn, still recovering from a pre-camp hamstring injury, took part in team drills Thursday, although the practice was largely a scout-team practice in preparation for the New York Giants on Saturday. Bowles said Flynn is not expected to play until the fourth preseason game.
Flynn didn't receive a ringing endorsement from Bowles at the time of his signing, with the coach saying they opted for him because he was the only experienced quarterback available. The Jets used their fourth-round pick on former Baylor quarterback Bryce Petty, but the rookie still has a ways to go.
"He has to progress," Bowles said when asked whether Petty can do something before the season opener to earn the backup job. "To say that he's going to get better in two weeks and be ready for the season is wrong.
"You just want him to get better. As the season goes and as the practices go, and he gets more comfortable, he will be ready when he's ready. It is not a two-week thing for him."
To make room on the roster for Johnson, the Jets waived undrafted rookie quarterback Jake Heaps.
Johnson, 29, has played for the Tampa Bay Buccaneers, Cleveland Browns, Bengals and San Francisco 49ers. His career numbers: 96-for-177, 1,042 yards, five touchdowns and 10 interceptions. His record as a starter is 0-5.
He didn't play in the Bengals' most recent preseason game. In the first game, he completed 11 of 21 passes for 175 yards.
Information from The Associated Press was used in this report.