"I think he's always contributed in a positive way to the league. Mal has really become a good friend and somebody that I have a tremendous amount of respect for. I'm happy for him. I'll be most happy for him if he can get healthy and be around here with us. But I'm going to miss him."
Saban said Moore had talked about stepping down for a while.
Alabama said it would hire a replacement as AD "as quickly as possible."
Moore oversaw an athletic department that made more than $200 million in facilities improvements — including two expansions of Bryant-Denny Stadium totaling about $112 million — and won national championships in football, gymnastics, softball and women's golf in 2011-12. The stadium now holds 101,821
The football building and his own memorabilia-covered office are housed in the Mal M. Moore Athletic Facility, named after him in 2007. Alabama opened a $9 million athletic training facility in February.
"Mal Moore is Crimson Tide sports," Bonner said. "During his tenure as athletics director, our student athletes have experienced unprecedented success in every aspect of their careers at UA, on the field of play and in the classroom. His contributions to UA athletics on every level are unsurpassed. And, while he will no longer be in charge of day-to-day operations, I am so pleased that we will continue to be able to rely on his wisdom and expertise going forward."
Moore was a freshman on Bryant's first Alabama team in 1958 then spent 22 seasons as a coach, including stints with the NFL's Cardinals in St. Louis and Phoenix and at Notre Dame.
He joined Bryant as a graduate assistant in 1964 and coached both the secondary and quarterbacks before becoming the Tide's first offensive coordinator in 1975. He was also Gene Stallings' offensive coordinator from 1990-93 in a tenure that included the 1992 national championship.