"The [Olympic committee] of Belarus is ordered to return to the IOC, as soon as possible, the medal, diploma and medallist pin awarded to the athlete in relation to the above-noted event," the IOC said in a statement.
The announcement came hours after the flame was extinguished at the Closing Ceremony with athletes and officials heading out of London. A day earlier, IOC President Jacques Rogge had proclaimed the fight against doping a success.
The Belarus team had already sent home hammer thrower Ivan Tsikhan because of suspicions over a sample provided after his silver-medal performance at the 2004 Athens Games.
Besides Ostapchuk, only one athlete tested positive for a banned substance after competing. U.S. judo fighter Nick Delpopolo was cited for traces of marijuana in his urine sample.
He blamed "inadvertent consumption" of food baked with the substance. The IOC disqualified him from seventh place in the 73-kilogram class.
Seven more were caught in doping controls conducted since the official testing period for the games began July 16. One of the seven competed in London before her test result was known.
"I think that is a sign that the system works," Rogge said Sunday. "I am happy about the fact that we could catch athletes who cheated, both before the Games and at the Games."
The IOC had said this would be its most extensive Olympic anti-doping program. It took almost 6,000 urine and blood samples, including no-notice tests ahead of athletes competing.