Mehdi Nemmouche, 29 – who has dual French and Algerian citizenship – has been held in police custody on anti-terror laws on suspicion of murder, attempted murder and possession of weapons since being arrested in Marseilles on 30 May.
Nemmouche opposed extradition fearing he would be sent on from Belgium to a third country for trial.
His lawyer, Apolin Pepiezep, has said that Nemmouche feared he would be sent to Israel, given that two of the victims of the attack were Israelis.
Nemmouche had previously been convicted of armed robbery, assault and vandalism, among other crimes in France, and spent most of 2013 in Syria fighting for Islamist rebels.
European governments are worried citizens going to fight in Syria will import Islamist militancy on their return.
In the Brussels attack an Israeli couple and a French woman were killed by a gunman who opened fire with a Kalashnikov. A Belgian man was also shot and injured and died on 6 June.
When arrested at a bus terminal, Nemmouche was carrying a Kalashnikov, another gun and ammunition but told police he had stolen them from a car in Brussels, his lawyer said.
Nemmouche has three days to appeal against the decision. If he does, the court will have 40 days to make a final ruling.
If he does not, he will be extradited at the end of that period. “He will most likely appeal the decision,” said Mr Pepiezep. “He has not received a guarantee from Belgium that he would not be extradited to a third country.”
An extradition within EU member states takes on average 16 days if the suspect agrees to it but any appeal is likely only to delay rather than block his transfer to Brussels.
At the time of the shooting, Nemmouche was also said to be carrying a camera with a 40-second video showing the two guns and a voice recording, claiming responsibility and expressing regret the device had not captured the shootings.
Since the incident, French president François Hollande has said France was determined to stop “jihadist” outrages.
“We will monitor those jihadists and make sure when they come back from a fight that is not theirs, and that is definitely not ours … they cannot do any harm,” he said.
Nemmouche hails from the northern town of Roubaix and was previously jailed for five years for robbery and released in December 2012. He is said to have associated with Islamists in jail, and spent a year in Syria from January 2013. He returned to Europe in March.
Belgian foreign minister Didier Reynders was one of the first at the scene of the killings. At the time, he said: “You cannot help think that when we see a Jewish museum, you think of an antisemitic act.
“But the investigation will have to show the causes.”