A spokeswoman for the Belgian police told AFP that Mehdi Nemmouche, a 29-year-old Frenchman of Algerian descent, "has arrived" in Brussels.
"He will be interrogated," added spokeswoman Tine Hollevoet, who declined all further details.
France's final appeals court last week cleared his extradition for questioning over the May 24 killings of a Jewish couple, a Frenchwoman and a Belgian man at the downtown Brussels museum.
Nemmouche initially had 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.
The shooting – the first such attack in Brussels in three decades – raised fears of a resurgence of anti-Semitic violence in Europe and of terror attacks from foreign fighters returning from Syria.
Nemmouche had spent more than a year fighting with Islamic extremists in Syria.
He was arrested on May 30 in the southern French city of Marseille after being spotted in a bus from Brussels.
A revolver and Kalashnikov rifle were found in his luggage, ressembling weapons caught on a museum video-camera, as was a portable camera