The second-round tender will cost the Browns $2.746 million for the 2017 season and net them a second-round pick if he receives an offer sheet from another team and they elect to pass on matching it.
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.