Egyptian authorities confirmed the find of the recorder on June 16 after pulling it from the Mediterranean by a search vessel.
Officials said the device had needed to be removed in several stages but that its memory unit was fully intact.
The equipment is now due to be taken to Alexandria for testing.
Investigators said: "The vessel’s equipment was able to salvage the part that contains the memory unit, which is considered the most important part of the recording device."
Deep sea ocean search vessel John Lethbridge is currently taking photographs of debris after it discovered "several main locations" of wreckage on the sea floor between Crete and the Egyptian coast on June 15.
It is still not known what caused flight MS804 to crash en route from Paris to Cairo on May 19 with 66 people onboard.
According to Greek investigators, the plane made two sharp turns before plummeting into the Med.
France’s aviation safety agency, BEA, has previously stated that the aircraft transmitted messages detailing smoke inside the cabin and a fault with its flight control unit before crashing.