He was wounded and arrested in a dramatic raid in Brussels on 18 March after four months on the run.
The 26-year-old French national was born in Brussels and lived there before the Paris attacks.
Some 130 people were killed and dozens wounded in co-ordinated attacks carried out by so-called Islamic State in Paris on 13 November.
The federal prosecutor said Salah Abdeslam had been "surrendered to the French authorities this morning (in execution of the European Arrest Warrant issued by France on 19 March 2016)".
It is not immediately clear where he has been taken, although it is known that he was transferred recently from prison in Bruges to the high-security jail at Beveren, near Antwerp.
Salah Abdeslam was indicted by Belgian authorities last week over a shoot-out in the Forest area of Brussels in which four police were wounded, three days before he was arrested.