Russian Federation is also seeking the extradition of Vinnik on suspicions of fraud, but there is still no date for the court hearing. If extradited to the US, Vinnik faces up to 55 years in prison.
Russian citizens Pyotr "Peter" Levashov, 36, and Alexander Vinnik, 37, were arrested earlier this year while vacationing in Spain and Greece, respectively, spurring separate but similar extradition battles at the center of this week's rulings.
United States officials charge that as the operator of BTC-e, Vinnik extensively laundered criminal proceeds thereby facilitating drug trafficking and hacking, accusations that he has repeatedly denied.
Russia's Prosecutor-General's Office requested Vinnik's extradition to Russian Federation.
While Vinnik denies all charges laid against him by both countries, he has consented to Moscow's extradition request, but challenged United States efforts to have him transferred to America.
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He is reportedly appealing the decision in Greece's supreme court. US authorities also accuse him of laundering funds obtained from the 2014 collapse of the Japan-based exchange Mt. Gox.
Russian Federation also demanded return of Vinnik, which was captured in a hotel near city of Thessaloniki, Greece.
"We have faith in the Greek justice system and a long road ahead of us", the Reuters news agency quotes Xanthippi Moisidou, one of Vinnik's lawyers, as saying.
"Through his actions, it is alleged that he stole identities, facilitated drug trafficking, and helped to launder criminal proceeds from syndicates around the world".
Vinnik claimed that he had nothing to do with the BTC-e.