Satellite data has confirmed Malaysia Airlines flight MH370 carrying 239 people crashed into the southern Indian Ocean.
Malaysian Prime Minister Najib Razak told a news conference all those on the Boeing 777-200 have been lost.
He said satellite data provided by UK company Inmarsat showed the plane's last recorded position was in the middle of the Indian Ocean, west of Perth, Australia.
"This is a remote location, far from any possible landing sites," Mr Razak said.
"It is therefore with deep sadness and regret that I must inform you that, according to this new data, flight MH370 ended in the southern Indian Ocean."
Sky's Jonathan Samuels in Beijing said there were "very, very distressing" scenes as relatives were told the news .
"Some people were in tears, others are helping those struggling and a woman is screaming in absolute anguish. It's very tough to watch," he said.
Malaysia Airlines told relatives they should "assume beyond any reasonable doubt" that all those on the plane are dead.
"Malaysia Airlines deeply regrets that we have to assume beyond any reasonable doubt that MH370 has been lost and that none of those on board survived," the airline said in a text message to relatives.
"As you will hear in the next hour from Malaysia's Prime Minister, we must now accept all evidence suggests the plane went down in the Southern Indian Ocean."
The mystery of what happened to the plane and why it veered west from its Kuala Lumpur to Beijing route remains unsolved.
Hijacking, pilot incapacitation and pilot murder-suicide are still all possible explanations.
China's foreign ministry has demanded Malaysia provide "all information and evidence" about the doomed flight.
The airliner vanished from civilian radar screens around 40 minutes after take-off from Kuala Lumpur on March 8.
No confirmed sighting of the plane has been made, but debris found in remote waters off Australia might be part of the missing plane.
An Australian navy ship is investigating sightings of floating objects some 1,550 miles west of Perth.
The objects are separate from several "suspicious" floating objects sighted by a Chinese search plane.
The crew of the military Ilyushin-76 aircraft saw "white and square" objects dispersed over several miles in the southern Indian Ocean.
They included two "relatively big" objects and several smaller ones.
The objects cited by the Chinese were seen near an area identified by satellite imagery as containing possible debris from the missing airliner.
The US Navy has also announced it is sending one of its high-tech black box detectors to the area.