US prosecutors are seeking Firtash, a one-time ally of ousted Ukrainian President Viktor Yanukovych, on allegations he led a conspiracy to pay $18.5 million to Indian officials to facilitate a mining project there.
The shock decision overturned a 2015 verdict by a lower court, which had rejected the USA request on the grounds that it was politically motivated.
News reports tie him to business dealings with lobbyist Paul Manafort, an adviser to Donald Trump during his USA presidential election campaign.
The dramatic arrest of one of Ukraine's richest men took place just after the appeals court in Vienna unexpectedly ruled that he should be handed over United States authorities.
Austrian Judge Christoph Bauer suggested in 2015 that the extradition request for Firtash was linked to attempts to weaken Yanukovych by stripping him of a key ally.
Firtash is also wanted by Spanish authorities on suspicion of links to organized crimes and laundering over 10 million euros.
"(The ruling) means simply that it's up to another country to decide whether he's guilty or not", judge Leo Levnaic-Iwanski said. His lawyers argued that he is caught up in a larger battle over the future of Ukraine, which is fighting a pro-Russian insurgency in its eastern regions.
Mr Firtash's five-man legal team, led by former Austrian justice minister Dieter Boehmdorfer, told the court the U.S. wanted to sideline their client as part of a strategy to reduce perceived Russian influence in Ukraine.
The court stressed that its ruling did not imply that Firtash was guilty of any crime.
The move dealt a blow to Firtash who had said he would "return home immediately" after the verdict, in comments made shortly before the decision. Austrian prosecutors appealed that ruling on behalf of the U.S.
Firtash is also connected to Paul Manafort, a political consultant who served as U.S. President Donald Trump's campaign manager for much of the election before being dismissed. "Mr. Firtash, a Ukrainian, is charged concerning a project in India that was never completed - a project entirely outside of the Unites States that had no effect on the United States and in which the United States has no legitimate interest".
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