As per ESPN's Jeff Dickerson;
Veteran RB Curtis Brinkley has passed physical and will sign a 1-year deal with #Bears, source confirms.— Jeff Dickerson (@ESPNChiBears) August 12, 2013
Brinkley is 5'9" and 208 pounds, so I wouldn't expect him to get any fullback reps like Unga, but he'll be a veteran tailback for the coaches to evaluate.
In his three years as a pro, all with San Diego, he has appeared in 23 games with 2 starts. Last year was his most productive as a pro, with 278 all purpose yards.