The revelation that flight MH370 ended in the southern Indian Ocean is based on new analysis by UK investigators and the British satellite firm Inmarsat, Malaysia's prime minister has said.
Najib Razak said relatives of the flight's 239 passengers and crew had been told of the "heartbreaking" news.
Inmarsat used new techniques to detect the plane's course, he said.
The UK's Air Accidents Investigation Branch, which probes serious civil aircraft incidents, was also involved.
Malaysia Airlines flight MH370 went missing after taking off from Kuala Lumpur on 8 March.
Mr Razak's announcement came as the international search effort reached a fifth day of operations in the southern Indian Ocean.
Inmarsat has told the BBC it gave the Air Accidents Investigation Branch (AAIB) the new data on Sunday - stressing it needed to be checked before it was made public.
The firm said its latest calculation involved a large amount of data analysis, focusing on a number of factors including the movements of other aircraft.
It involved an entirely new way of modelling which is why the analysis took some time, the firm said.
Inmarsat senior vice-president Chris McLaughlin said the firm had studied electronic "pings" - or bursts of data - which the plane had sent to one of its satellites.
He told the BBC: "We have been dealing with a totally new area. We've been trying to help an investigation based on a single signal once an hour from an aircraft that didn't include any GPS data, any time and distance information.
"So this really was a bit of a shot in the dark and it's to the credit of our scientific team that they came up and managed to model this."
Mr McLaughlin continued: "They managed to find a way in which to say just a single ping can be used to say the plane was both powered up and travelling, and then by a process of elimination - comparing it to other known flights - establish that it went south."
A spokeswoman for the AAIB said it could not comment on the investigation, but confirmed: "As set out by the Malaysian prime minister, we have been working with the UK company Inmarsat, using satellite data to determine the area on which to focus the search."
Oceanographer Dr Simon Boxall, from the University of Southampton, told the BBC: "The algorithms and the techniques [Inmarsat] have applied to try and locate - to within a certain area - where the last transmission was made is really quite phenomenal - but also quite tragic because it does show this plane was heading to an open area of ocean."
He continued: "They've probably crammed almost a year's worth of research into maybe a couple of weeks, so it's not a routine calculation they would ever, ever make.
"They've been looking at all the signals they have, all the recordings they have, and processing that many times over to try and pinpoint where the plane's signal came from. Technologically it's really quite astounding."
But Philip Baum, editor of Aviation Security International Magazine, said the mystery of the missing Boeing 777 jet had not been solved.
"We still believe there was a deliberate act that took place on board the flight deck inside the cockpit that resulted in the aircraft turning and heading south," he said.
"So until we find the black box we're really not going to know anything more."
Mr Razak told a news conference in Kuala Lumpur that work by the AAIB and Inmarsat had revealed MH370's last position was in the ocean west of Perth, Australia.
"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," he said.
He added that for the relatives of those on board, "the past few weeks have been heartbreaking. I know this news must be harder still".
Malaysia Airlines said all relatives of those on board had been informed "face-to-face by our top management", as well as by text message.
Boeing said in a statement: "Our thoughts and deepest sympathies continue to be with the families and loved ones of those aboard."
British Royal Navy ship HMS Echo is due to arrive in the area on Tuesday to help with the search.