The Vilnius Court of Appeal said Dmitry Ustinov, who was arrested at Vilnius International Airport in April at the request of the US, should be handed over to American officials within 10 days. The decision cannot be appealed.
Prosecutors said the 47-year-old Ustinov is suspected of smuggling and operating a group that attempted to export military equipment illegally. The criminal charges could send him to prison for up to 20 years.
The decision was condemned by the Russian government, which had demanded that Ustinov not be extradited.
"We do not intend to accept this lawlessness in relation to our citizens, who have become victims of this specific form of American 'justice,'" Dolgov said in a statement. "We hope that Washington will think about the consequences of its actions.