The court decision overturns a lower court ruling nearly two years ago against extraditing Dymitro Firtash.
The judge then said that the US move was at least partially politically motivated through links to political events in Ukraine, and not supported by sufficient evidence.
Extradition, however, is still not a certainty. Leo Levnaic-Iwanski, who headed the judges' panel of the Upper State Court, said the final decision will be made by Justice Minister Wolfgang Brandstetter.
Firtash was indicted in Chicago by a US grand jury in 2012 for allegedly paying off officials through US banks in a failed attempt to secure titanium mining rights in India.
One of Ukraine's most influential businessmen, Firtash, 51, is well connected both in Moscow and with Ukrainian politicians opposed to the Kremlin. He earned millions of dollars in the natural gas trading sector under deposed pro-Russian Ukrainian President Viktor Yanukovych.
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