Olson left the team Nov. 4, citing personal reasons, including a divorce. On Monday, while announcing that he would return as head coach when the current season ends, Olson also said his absence was health-related.
He said he had "a medical condition that was not life-threatening but serious enough to require time away from my coaching responsibilities."
The Wildcats are 18-13 this season under interim coach Kevin O'Neill and meet Oregon State in the first round of the Pac-10 Tournament this week.
Olson, 73, has compiled a 780-280 career record at Arizona, Iowa, and Long Beach State. His 589-187 record with the Wildcats includes the 1997 national championship, four Final Four appearances, 11 Pac-10 titles, and 20 consecutive 20-win seasons. Olson has also won seven Pac-10 Coach of the Year awards.
Inducted into the Basketball Hall of Fame in 2002, Olson also guided Iowa to the 1980 Final Four.