Mehdi Nemmouche, 29, had filed an appeal against a June ruling that ordered his extradition from France, but his lawyer Apolin Pepiezep said he had decided not to go ahead with the challenge.
Pepiezep had until July 7 to file appeal documents but said that after consideration he found the ruling "satisfactory" because it contained guarantees Nemmouche could not be sent to another country from Belgium.
"My client could not be extradited from Belgium to a third state without the agreement of the French authorities," he said.
The French courts can now authorise Nemmouche's extradition, which can take place within 10 days of a court order.
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 in a bus coming from Brussels.
A Paris court meanwhile today convicted four men of fighting with Islamic extremists in the Pakistan-Afghanistan border region.
The court sentenced Touhami Tebourski, a 32-year-old Tunisian who fought with the Taliban and is currently in prison in Turkey awaiting extradition to France, to nine years in prison.
Two others in court were sentenced to eight years in prison while a fourth man was tried in absentia and is believed to be on the run in Tunisia.
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