The 25-year-old, named as Benjamin F., was detained in late April at the Polish border post of Dorohusk as he was trying to cross over into Ukraine.
The ex-Austrian army soldier is alleged to have killed unarmed prisoners while fighting on the Ukrainian side against Russia-backed separatists in May 2016.
Austrian authorities had issued a European arrest warrant in February after he gave an interview to Austrian newspaper Der Kurier about his activities in Ukraine.
The suspect was extradited on Monday and is "currently in police custody", said Erich Habitzl, spokesman for the prosecutor's office.
More than 10,000 people have been killed since the start of a pro-Russian insurgency in April 2014 which Kiev and the West accuse Moscow of masterminding.
Although the violence has ebbed in the wake of several ceasefire accords, efforts to secure a peace deal have ground to a halt amid sporadic clashes, and neither side appears prepared to make concessions.