The IOC also confirmed Nigeria were awarded the gold medal at the 4x400m men's relay race from the Sydney 2000 Olympics after it closed the case on doping offender Antonio Pettigrew of the US.
Cox, the Athens relay alternate, was banned for four years in 2010 for using performance-enhancing drugs. The US Anti-Doping Agency had said Cox had used prohibited anabolic agents between 2001 and 2004.
The IOC's Executive Board, however, did not make any decision on the other relay runners in the team, saying it was up to the International Association of Athletics Federations to decide if all the runners on the US team would be stripped of their medals.
Russia were second in that race and Jamaica won bronze. Britain finished fourth. Should the IAAF decide, as it has done in similar cases, to strip the medals from all team athletes, these countries will be moved up to gold, silver and bronze.
The other members of the US 4x400 team from 2004 were Monique Henderson, Monique Hennagan, Sanya Richards and Deedee Trotter.
Pettigrew, who committed suicide in 2010, had been disqualified in 2008 from the 4x400m race in Sydney where the United States won gold with a team that which included Michael Johnson and the 400m race where he finished seventh. Pettigrew had admitted to doping.
The IOC had delayed reallocating the medals, awaiting any new information from an ongoing investigation into an American doping scandal.
It said given that no new information was provided it proceeded with awarding Nigeria the gold medal. Jamaica were moved up to silver and the Bahamas awarded the bronze medal.