Mbarushimana is the executive secretary of the FDLR, a Rwandan Hutu rebel group that which operates in eastern Congo.
The ICC has issued an arrest warrant for him on charges of murder, rape, torture and destruction of property in the east of the Democratic Republic of Congo in 2009.
He denies the charges.
He was arrested in France last year and a French court approved the transfer to the Hague on 4 January.
Mbarushimana was charged in December of crimes against humanity by a French judge. He had been living in the country as a political refugee since 2002.