Firtash is wanted in the U.S. over allegations that he paid some US$ 18.5 million in bribes for a permit to mine titanium in India, media reported.
Firtash was first arrested in Vienna in 2014 at the request of the FBI which also sought his extradtion.
A lower court in Austria rejected the request, claiming it was at least partially politically motivated and that the United States had not provided enough evidence.
Firtash was released after paying a record bail of US$ 172 million waiting for his case to be resolved.
Then on Tuesday, the Vienna court overturned the lower court decision and approved the extradition request which left Firtash, his wife Lada and his entourage occupying the entire first row breathless, according to Austrian media reports.
"This does not mean that somebody is being prejudged as guilty, but rather that this will be decided in another country," the judge told a courtroom filled with journalists.
The Austrian Minister of Justice is now to make a final decision on Firtash's extradition.
Firtash — Ukraine’s 16th richest man with estimated wealth of $251 million as of 2016 — is the co-owner of RosUkrEnergo, a Swiss-registered company that transports natural gas from Central Asia to Eastern European countries.
A former supporter of deposed pro-Russian Ukrainian President Viktor Yanukovich, Firtash made his fortune selling Russian gas to the Ukrainian government, according to Reuters.
In a 2014 video, Firtash denied the bribery allegations, claiming he was stuck in the middle of a "battlefield for the two biggest global players of Russia and the United States."
Before Tuesday’s verdict, Firtash’s lawyer Dieter Boehmdorfer reiterated that the case was political, adding that Firtash was the victim of a United States strategy to curtail Russia’s influence in Ukraine, Reuters reported.
Yanukovich was ousted in February 2014 after mass street protests, known as the EuroMaidan Revolution. The United States welcomed his ouster and backed his pro-Western successor, Petro Poroshenko.
Spain has also filed an extradition request for Firtash to face trial for alleged money laundering, Kyiv Post reported.
