The Jets also exercised options on pass rushers Calvin Pace and Jason Babin.
Johnson, 29, signed with New York after six seasons with the Tennessee Titans. With the Jets, he scored just one touchdown on the ground and totaled 663 yards, ceding the majority of carries to Chris Ivory.
Pace accumulated five sacks for the Jets in his seventh season with New York and 12th in the NFL. The 34-year-old has started all 16 games in four consecutive seasons.
Babin had two sacks in 16 games (four starts) in his first season with the Jets. In 11 seasons, the 34-year-old Babin has 64 1/2 sacks with the Jets, Jaguars, Eagles, Titans, Seahawks, Chiefs and Texans.