The 5-foot-11, 203-pound safety from Alabama was the 95th selection overall.
Johnson, a walk-on out of high school, was a leader of the powerful Crimson Tide defense and is expected to fight for the backup role behind Adrian Wilson and Antrel Rolle and for a spot in the Cardinals' nickel defense.
Johnson was an Alabama captain as a junior and senior. He was second on the team in tackles with 89, 60 solos, along with five interceptions, a sack, a forced fumble and a fumble recovery.
He was a unanimous all-SEC selection and was a second-team Associated Press all-American.
In another move, Arizona released wide receiver Shane Morales, who had signed as an undrafted rookie free agent out of Oregon State on April 27.
The defending NFC champions report for training camp in Flagstaff on July 29.