The state prosecution said in a statement, without giving further details, that the court has decided to transfer both men to France.
Abrini, long sought in connection with the November 2015 attacks in Paris which killed 130, was arrested in Belgium on April 8.
He later confessed to being the surviving bomber who fled Brussels airport on March 22, when more than 30 were killed in coordinated attacks at the airport and an underground station in the Belgian capital.
A European Arrest Warrant was issued at France's request last week for Abrini, as well as suspects identified as Hamza A, Mohammed A, Ali O and Mohamed Bakkali.
Abrini's exact role in the Paris killings is not known.
He was spotted with key suspect Salah Abdeslam in the preceding days, and his fingerprints and DNA were found in a car used in the attacks, as well as at terrorist hideouts in Brussels.
Abdeslam was also arrested in Brussels, days before the attacks in the Belgian capital, and is now in French custody.