Arians reached an agreement on a four-year contract with a team option for a fifth, the Cardinals said, without disclosing financial terms.
Arians, 60, was the offensive coordinator for the Colts and substituted in 12 National Football League games for coach Chuck Pagano while he was treated for leukemia.
The Cardinals released Ken Whisenhunt the day after they finished the 2012 season with a 5-11 record.
Arians joined the Colts after spending eight seasons with the Pittsburgh Steelers. He also was an assistant coach for New Orleans and Kansas City.
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