Córdoba made his debut with the Colombian Serie B team Deportivo Rionegro in 1993, his subsequent performances earned him a transfer to Colombian heavyweights Atlético Nacional in 1996. He made his name playing for San Lorenzo in Argentina from 1998 but signed for Italian side Internazionale in the winter transfer window, January 2000, costing the club €16 million, rejecting another offer from Real Madrid in doing so. He has become a mainstay of the Internazionale defence for several years, forming a highly effective partnership in central defence with Marco Materazzi. His long career at Inter led him to be named the club's vice-captain behind Javier Zanetti; because of this, he had the honour of lifting the Coppa Italia in 2005 when Zanetti was absent due to his involvement in the Confederations Cup with Argentina.