They were picked up by the French vessel Laplace as it was searching the Mediterranean Sea.
There were 66 people on board when the Airbus A320 crashed on 19 May while flying from Paris to Cairo.
It vanished from Greek and Egyptian radar screens, apparently without having sent a distress call.
“The signal from a beacon from a flight recorder has been detected,” said Remi Jouty of France’s Bureau of Investigations and Analysis.
A priority search area has been established, he added.
Laplace is using acoustic detection systems to listen to the locator “pings” given off by the black boxes underwater.
A specialist vessel carrying robots able to dive to 3,000 metres (3,280 yards) is due to arrive next week to help retrieve the devices.
Egyptian investigators first reported that the French vessels had picked up signals from the wreckage search area, saying they were “assumed” to be from one of the devices.
Officials from the country said last week signals from the plane’s emergency beacon had been detected but later said they were received on the day of the crash and were not new.
What caused the crash remains a mystery. Finding the black boxes is crucial to piecing together what happened in the plane’s final moments.
A militant attack has not been ruled out but no extremist group has claimed the downing of the plane.
Human or technical error is also a possibility. Flight data revealed that smoke detectors went off in the toilet and the aircraft’s electrics, minutes before the plane’s signal was lost.
The recorders are not waterproof so the circuits in the box have to be thoroughly dried out before they try to access the contents.
And that is assuming the data or voice recordings survived the crash.
If they have found a black box, it will either be the one containing technical data or the one recording the last two hours of sound in the cockpit.
That may give them enough to rule out certain things, like whether someone stormed the controls, or whether a bomb went off. But it could still leave questions.
The clues so far point to an on board fire. The black boxes could confirm that, but they might not reveal whether it was a malicious act or a horrible accident.
Black boxes emit signals for 30 days after a crash, giving search teams an ever-narrowing window to locate them before their batteries run out.
Debris from the plane has been recovered from the sea, some 290km (180 miles) north of the Egyptian port city of Alexandria.
But the bulk of the plane and the bodies of passengers are thought to be deep under the sea.
Those on board MS804 included 30 Egyptians, 15 French citizens, two Iraqis, two Canadians and citizens from Algeria, Belgium, Britain, Chad, Portugal, Saudi Arabia and Sudan.