Dunbar started in 12 games for the Frogs last season, moving around the offensive line throughout. The 6-foot-6, 315-pound lineman started seven games at left tackle and five at left guard.
The New Boston, Texas, native also received his degree from TCU over the weekend. Dunbar was previously dismissed from the team in 2012 due to academic issues.
Dunbar later returned to the Frogs for the 2013 campaign.
TCU head coach Gary Patterson has had 34 players drafted, with 71 in NFL camps. ESPN.com recently ranked TCU as the top school in the nation for developing NFL talent, according to the release.
The Bears went 8-8 and ranked fifth in passing yards per game (267.6), according to ESPN.