Johnson spent the last four seasons with the Cardinals and became a free agent after last season. The 2009 third-round draft pick out of Alabama is expected to start at strong safety after taking the job from Adrian Wilson late last season.
Wilson, a five-time Pro Bowl selection, was released by Arizona last week.
Johnson had a career-best two interceptions last season with 15 tackles and a fumble recovery in 15 games, three as a starter.
He returned an interception for 57 yards for his first career NFL touchdown last season.