The belts had been taken from the retired boxer's Mission Hills home in March 2012, the Los Angeles Times reported Monday.
Detectives allegedly found them in the bottom of a clothes hamper at the home of convicted burglar Jose Pedraza, who was in the process of being deported when he was tracked down, the newspaper said. Los Angeles police found Pedraza using fingerprints he allegedly left on a mirror in Barber's home.
"When the print report came in, we had to act fast," Det. William Cooper said in a statement.
"Unlike the other burglaries, Pedraza was not copping out to this one, and it seemed like he was in a hurry to get out of the country, like he was trying to avoid something," Cooper added.
Barber won one of the belts for the International Female Boxers Association super featherweight title in 2010 after she beat a South Korean opponent, the Times reported.
Barber said she and her husband's wedding rings were also stolen in the March 2012 burglary, though police did not find them with the belts.