The 28-year-old running back was released by the Tennessee Titans earlier this month having recorded a career-low 3.9 yards per carry last season.
Despite a poor campaign, a number of teams were interested in Johnson, but he signed for the Jets on Wednesday, having passed his medical the previous day.
Upon signing, he told The Tennessean: "I have a fresh start. Now I am going to go out there with a chip on my shoulder. I know a lot of people are doubting me. I want to prove everybody wrong who has doubts in me.
"The Titans were ready to move on. They didn't want me any more, but everything is going to work out. I am very excited about joining the Jets.
"It's a team on the rise and I want to make them better. I still have the ability to do that."
He rushed for over 2,000 yards during the 2009 season.