Terms were not disclosed Wednesday.
Taken in the seventh round of the supplemental draft, Unga is BYU's all-time leading rusher with 3,455 yards on 696 carries. He also caught 102 passes for 1,085 yards over four seasons and had 45 touchdowns — 36 rushing and nine receiving.
The Bears have also cut defensive tackle Jimmy Saddler-McQueen and wide receiver Vic Hall. They were undrafted free agents.