The school says the 73-year-old Moore died on Saturday at Duke University Medical Center. Moore had been in the Durham, N.C., hospital since March 13 with pulmonary problems.
He had been part of 10 football national championships as a Crimson Tide player, coach or administrator. Moore was athletic director since 1999 before stepping down March 20 because of the health problems.
The football and athletic administration building bears his name, but his biggest claim to fame might have been hiring Nick Saban as football coach. Saban has led the Tide to three titles in four years.
Moore was an assistant coach under Bear Bryant and Gene Stallings, and played on Bryant's 1961 national championship team.