Firtash already posted 125 million euros (USD 132 million) bail and surrendered his passport three years ago when the US extradition request was first made.
The court today cited these measures in reaching its decision.
Firtash was indicted 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 worth hundreds of millions of dollars.
He was taken into custody on Tuesday shortly after another court approved the US request and legal authorities received a separate application from Spain.
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