Belgian police immediately interrogated Nemmouche, a 29-year-old Frenchman of Algerian descent, following Tuesday's move, but he refused to confess to having fired on the museum and killing four people on 24 May.
France's final appeals court last week cleared his extradition for questioning over the murder of a Jewish couple, a Frenchwoman and a Belgian man at the downtown Brussels museum.
Nemmouche had spent more than a year fighting with Islamist militias in Syria.
He was arrested on 30 May in the southern French city of Marseille after being spotted in a bus from Brussels.
He had initially filed an appeal against his extradition but then dropped his objection after guarantees that he would not be sent on to another country such as Israel from Belgium, according to his lawyer.