Malaysia's prime minister has announced that missing flight MH370 crashed in the southern Indian Ocean.
Najib Razak said this was the conclusion of fresh analysis of satellite data tracking the flight.
Malaysia Airlines had told the families of the 239 people on board, he said.
The BBC has seen a text message sent to families by the airline saying it had to be assumed "beyond reasonable doubt" that the plane was lost and there were no survivors.
There were 227 passengers on flight MH370, many of them Chinese.
Relatives of those on board who watched the announcement at a Beijing hotel wept with grief, and some were taken away on stretchers by medical teams, news agencies reported.
Flight MH370 disappeared after taking off on 8 March from Kuala Lumpur.
A big international search operation has been taking place in the southern Indian Ocean, along the southern arc or corridor of the plane's possible route, more than 1,500 miles (2,500km) off the south-west coast of Australia.
In the past day, both Australian and Chinese air force crews have reported spotting debris.
The unidentified objects have been seen in separate parts of the vast search area, in some of the world's most treacherous and remote waters.
The revelation by Prime Minister Najib Razak came at a late-night news conference in Kuala Lumpur.
It was based on new analysis by British satellite firm Inmarsat, which provided satellite data, and the UK's Air Accidents Investigation Branch (AAIB).
The firms "have concluded that MH370 flew along the southern corridor, and that its last position was in the middle of the Indian Ocean, west of Perth," Mr Razak said.
"This is a remote location, far from any possible landing sites. 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."
Mr Razak appealed to the media to respect the privacy of the families of the passengers and crew, saying the wait for information had been heartbreaking and this latest news harder still.
The text message sent to families by Malaysia Airlines announcing the loss of the plane said: "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... we must now accept all evidence suggests the plane went down in the Southern Indian Ocean."
Selamat Omar, the father of a 29-year-old aviation engineer who was on the flight, said some family members of other passengers broke down in tears at the news.
"We accept the news of the tragedy. It is fate,'' Selamat told Associated Press in Kuala Lumpur.
Fresh analysis methods
The Malaysian prime minister said Inmarsat had been able to shed further light on the plane's flight path by performing further calculations on the MH370 data "using a type of analysis never before used in an investigation of this sort".
According to Inmarsat, this involved a totally new way of modelling, which was why it took time.
The company told the BBC the new calculation involved crunching far more data, which included what other aircraft were doing at the time.
Inmarsat gave the AAIB the new data on Sunday, it said, which had to be checked before it could be made public.
Officials said earlier that the plane automatically sent an hourly "ping" - a brief signal - to the Inmarsat satellite even after other communication systems on the plane shut down.
Initial analysis showed the location of the final "ping" was probably along one of two vast arcs running north and south.