Gibbs, who has 19 U.S. caps, was signed by Charlton Athletic of the EPL in 2006 but saw no action because of a knee injury.
He was last active in 2005-06 season, when he saw limited time for Dutch club ADO Haag. In the 2004-05 season he played 15 games for Feyenoord of the Dutch Eredivisie.
"Any time you can add a defender with experience at a high level it is a positive," Rapids coach Fernando Clavijo said. "Cory is a solid player and can play both centrally and wide on the backline and will add leadership to the team."
Colorado, No. 2 on the allocation list, was able to acquire Gibbs after Los Angeles passed.
Gibbs passed his physical examination and could play on Saturday against Kansas City Wizards.