The Cardinals signed Reed to a one-year contract. Sources told the NFL Network the deal is worth about $2 million.
Reed is a native of Tucson, Ariz., and played collegiately at the University of Arizona.
Reed played the last four seasons with the Falcons. He saw snaps in all 16 games last season and recorded 24 tackles, one sack and a forced fumble. He also spent four seasons with the Houston Texans.
The signing is the second this week for the Cardinals, who also locked up former Falcons cornerback Robert Alford with a three-year deal Thursday. Atlanta cut Reed and Alford to free up salary-cap space.
Reed served as a defensive end with the Falcons, but is likely to switch to linebacker in the Cardinals' 3-4 defensive scheme.
The 32-year-old Reed has 21.5 sacks in his eight-year NFL career.