The second-round tender will cost the Jets $2.746 million for the 2017 season.
Johnson is expected to take over for long-time Jets C Nick Mangold.
Johnson, 26, is a former fifth-round pick of the Steelers back in 2014. He lasted just a few month in Pittsburgh before he was waived and later claimed by the Jets.
In 2016, Johnson appeared in 15 games for the Jets. Pro Football Focus graded him as the No. 33 overall center out of 38 qualifying players.