Unga led BYU in career rushing yards, and he led the Mountain West Conference with 1,087 rushing yards in 2009.
As a result of today’s pick, the Bears will give up a seventh-round pick.
Unga is expected to compete with Garrett Wolfe, Khalil Bell and rookie free agent Brandon Minor for a backup spot on the roster.
The Bears currently have two fullbacks under contract: Eddie Williams and Will Ta’ufo’ou, after releasing veteran Jason McKie earlier in the offseason. The Bears were one of 20 teams to attend Unga’s workout in front of NFL scouts prior to the supplemental draft.