NFL Network's Ian Rapoport added Johnson's deal is expected to pay out an average of $15 million annually.
Johnson, 28, was selected in the third round of the 2012 draft by the St. Louis Rams, and he spent the first six years of his career with the franchise, including the last two in Los Angeles after the team moved to Southern California.
However, signs had been pointing toward a possible split between the sides for some time.
Although the Rams paid Johnson $16.7 million to play on the franchise tag last season, that was reportedly what the front office was comfortable with shelling out to see how he performed under new defensive coordinator Wade Phillips.
According to Yahoo Sports' Charles Robinson, the Rams would not have kept Johnson had Phillips not joined the fray.
Johnson ultimately proved solid as the No. 1 corner for L.A.'s 13th-ranked pass defense and finished the year with 65 total tackles, two interceptions, 13 pass breakups and a forced fumble.
Despite that quality campaign, it became clear the Rams didn't envision Johnson as part of their future when they agreed to acquire cornerback Marcus Peters from the Kansas City Chiefs and Aqib Talib from the Denver Broncos, per Schefter.
For the Jets, though, Johnson addresses a major need.
New York finished last season ranked 21st against the pass, and the team had to nab a quality boundary corner with Morris Claiborne no longer under contract.
But now that Johnson is in the fold, the Jets have a true No. 1 corner who should strengthen a young secondary that flashed serious potential last season with the safety tandem of Jamal Adams and Marcus Maye holding things down on the back end.
And while the Jets could stand to add more depth at corner in the coming weeks, to be sure, nabbing Johnson is a major win.