The ICC issued a warrant to have Mbarushimana stand trial there for murders, rapes and torture allegedly committed in the eastern Democratic Republic of Congo in 2009 by the FDLR rebel force he used to lead.
He denies the charges.
The Paris appeals court approved his transfer to the ICC "on condition that under no circumstances should Mr Mbarushimana be taken back by any means to Rwanda".
Mbarushimana had been living in France as a refugee since 2002.
He was arrested last month on the ICC warrant.
His lawyers tried to block the warrant, arguing it could be a first step towards sending him back to Rwanda, where they said he would not get a fair trial.