Arizona coach Sean Miller said the hiring was well deserved.
Whitford, who is from Madison, Wis., coached in the MAC at Miami of Ohio and was with Miller at Xavier.
Ball State fired Billy Taylor last month, a day after losing to Buffalo in the Mid-American Conference tournament. Taylor was hired in 2007 to clean up a program coming off a school-record 22-loss season, awaiting an NCAA ruling and had been tainted by the former coach's accusations that racially charged letters had been left underneath his office door.
The Cardinals were 15-15, including 8-8 in conference play. Taylor went 84-99 in six seasons.
Arizona (27-8, 12-6 Pac-12) advanced to the Sweet 16 before losing to Ohio State.
Information from The Associated Press was used in this report.