USC had been banned from associating with the former Heisman winner due to NCAA sanctions.
Daniels is keeping open the possibility of returning to USC.
USC president Carol L. Folt credits Bohn for his 'diversity and breadth of experience' while stressing integrity for an athletic program recently mired in controversy.
Bohn, who helped Colorado join the Pac-12, has overseen the Bearcats' programs the past five years and would replace Lynn Swann as the Trojans' athletic director.
Dave Roberts will serve as the interim athletic director.