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 forego a seventh-round
With Matt Forte and Chester Taylor penciled in atop the Bears' depth chart at running back, 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 were one of 20 teams to attend Unga's workout in front of NFL scouts prior to the supplemental draft.
ESPNChicago.com Bears reporter Jeff Dickerson contributed information to this report.