Firtash, 49, one of Ukraine's richest men and previously a supporter of ousted president Viktor Yanukovych, was arrested in Austria in March 2014.
He was freed on bail 10 days later for 125 million euros (USD 139 million), a record for Austria, but has had to stay in the country.
US authorities want him extradited to face charges that he and five others paid USD 18.5 million in bribes to Indian officials to secure titanium mining licences in 2006.
Presiding judge Christoph Bauer said yesterday there was "no political influence" over the decision which "was taken on a legal and factual basis".
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Firtash owns Group DF, a business empire involved in energy, chemicals, media, banking and property in Ukraine and other countries including Germany, Italy and Austria.
He made his fortune importing gas to Ukraine from Russia and Central Asia via his group Rosukrenergo, since disbanded, in collaboration with Russian gas giant Gazprom.
Having backed the 2010 election campaign of Yanukovych, Firtash was able to expand his business interests, acquiring chemicals and fertiliser factories as well as TV channel Inter.