Bodies of the 10 crew members were handed over on Saturday, they said. Passengers would follow next week.
Investigators say traces of explosives have been found on the victims and a criminal investigation will be held.
Flight MS804 from Paris to Cairo plunged into the sea on 19 May killing all 66 people on board.
EgyptAir flight MS804: What we know
Among those who died were 40 Egyptians and 15 French nationals.
France has voiced concern about the delay in returning the bodies of its nationals.
French investigators have complained about co-operation with their Egyptian counterparts.
The Paris prosecutor opened a manslaughter investigation into the crash in June.
In September, French newspaper Le Figaro reported that French investigators had found trace levels of the explosive material TNT on debris of the plane, but had been prevented from examining it further.
Egyptian officials denied obstructing French inquiries.
The cause of the crash remains unclear. No distress call was made beforehand but the cockpit voice recorder revealed the pilots had fought to put out a fire.
Automated electronic messages sent out by the plane showed smoke detectors going off in a toilet and in the avionics area below the cockpit, minutes before the plane vanished.
Recovered wreckage showed signs of damage caused by high temperature and there was soot on the jet's front section.
Although there were fears that an act of terrorism might have brought the plane down, no group has said it targeted the plane.
The crash came seven months after a Russian passenger plane was brought down by a bomb over Egypt's Sinai peninsula, killing all 224 people on board.
An Egyptian affiliate of the Islamic State group said it was behind that attack. However, there was no such claim following the crash in May.
The EgyptAir plane had taken off from Paris' Charles de Gaulle airport where security has been tight since the jihadist attacks of November 2015.
Analysts say that in the two days before the crash, the plane had travelled to Egypt, Tunisia and Eritrea, leaving open the possibility that a bomb could have been planted before its arrival in Paris.
The bodies of the victims of the EgyptAir plane which crashed in the Mediterranean in May are being returned to their families, officials say.