Johnson's agent, Doug Hendrickson, announced the deal on Twitter.
The 30-year-old has bounced around the league in recent years and spent last season with the Giants, though he hasn't thrown a pass in an NFL game since 2011.
The 2008 fifth-round pick began his career with the Tampa Bay Buccaneers. He started four games as a rookie but struggled, with just a 50.4 percent completion rate and eight interceptions to go with four touchdown passes.
With a 0-5 career record as a starter, he has settled nicely into a backup role, where he has spent time with the Cleveland Browns, Cincinnati Bengals, Baltimore Ravens and more. He joined the Giants in September after getting cut by the Ravens in the preseason.
Despite the lack of recent game experience, he remained confident as the Giants' No. 2 quarterback down the stretch.
"I play football, man," Johnson said in December, per Tom Rock of Newsday. "Football is football to me. That's how I look at it. In practice, every time you have an opportunity to work on your craft, it's about putting yourself in the mind frame where you get the reps. It's not trying to make the situation too big or too small. Just do what you know and trust your training."
Considering Manning hasn't missed a start since earning the job in his rookie season, playing time will remain tough to come by for Johnson.