Mukhtar Ablyazov, who was chairman of Kazakh bank BTA, had been in hiding since being sentenced to prison for contempt of court by an English judge 18 months ago.
He was arrested in Aix-en Provence in the south of France last July and has been held in custody there since.
BTA said both Ukraine and Russia wanted to pursue criminal charges in relation to frauds committed against the bank in those jurisdictions.
It welcomed what it said was a “landmark decision”, saying that it would force “Mr Ablyazov to face justice for his actions”.
Chris Hardman, partner at Hogan Lovells and the bank’s lawyer in London, said it demonstrated Ablyazov’s attempts to portray the bank’s motivations as political were “groundless”. “He is merely being required to answer for the billions of dollars that were taken from BTA and its creditors,” he added.
Ablyazov denies the allegations, arguing they are politically motivated and designed to eliminate him as a rival to Kazakh President Nursultan Nazarbayev. His family say his life would be in danger if he were sent back to Kazakhstan.
“French justice is not doing itself an honour. Either it’s very naive about states widely recognised as corrupt or it (the ruling) is a sign of the political powers’ sway over the court,” said Bruno Rebstock, one of Ablyazov’s lawyers. BTA was seized by Kazakh authorities and declared insolvent in 2009.
Ablyazov was granted political asylum by the UK in 2011, but fled London last year after being sentenced to prison for contempt of court.