Citing groundbreaking satellite-data analysis by the British company Inmarsat, Malaysian Prime Minister Najib Razak said
His statement may go some way toward tamping down some of the more fevered speculation about the plane's fate, including one theory some grief-stricken relatives had seized on: that the plane had been hijacked and forced to land somewhere.
All 239 people on board were presumed dead, airline officials said on Monday.
Najib's announcement opens the way for what could be one of the most costly and challenging air crash investigations in history.
The launch of an official air crash investigation would give Malaysia power to coordinate and sift evidence, but it may still face critics, especially China, which had more than 150 citizens on board the missing plane and has criticised Malaysia over the progress of the search.
The Inmarsat data showed the Boeing 777's last position was in the Indian Ocean west of Perth, Australia, Najib said in a statement.
"This is a remote location, far from any possible landing sites," he 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."
Chinese Deputy Foreign Minister Xie Hangsheng immediately demanded all relevant satellite-data analysis from Malaysia that demonstrated how Malaysia had reached its conclusion about the fate of the jet.
In a further sign the search was bearing fruit, the U.S. Navy was flying in its high-tech black box detector to the area.
The so-called black boxes - the cockpit voice recorder and flight data recorder - record what happens on board planes during flight. At crash sites, finding the black boxes soon is crucial because the locator beacons they carry fade out after 30 days.
Flight MH370 vanished from civilian radar screens less than an hour after taking off from Kuala Lumpur on March 8. No confirmed sighting of the plane has been made since and there is no clue what went wrong.
Attention and resources in the search for the plane had shifted from an initial focus north of the Equator to an increasingly narrowed stretch of rough sea in the southern Indian Ocean, thousands of miles from the original flight path.
Investigators believe someone on the flight may have shut off the plane's communications systems. Partial military radar tracking showed it turning west and re-crossing the Malay Peninsula, apparently under the control of a skilled pilot.
That led them to focus on hijacking or sabotage, but investigators have not ruled out technical problems.
Relatives of those on board received the news that the search for survivors was over in a Malaysia Airlines SMS message which said: "We have to assume beyond all reasonable doubt that MH370 has been lost and none of those on board survived."
After the message was transmitted, there were hysterical scenes at the Beijing hotel where many of the relatives of those on board were staying.
A Reuters reporter on the scene saw at least four people being carried away on stretchers.
Najib's comments came as an Australian navy ship was close to finding possible debris from the jetliner after an increasing number of sightings of floating objects that were believed to be parts of the plane. The search site is about 2,500 km (1,550 miles) southwest of Perth, in icy sub-Arctic seas that are in one of the most remote parts of the world.
The objects, described as a "grey or green circular object" and an "orange rectangular object", were spotted on Monday afternoon, said Australian Prime Minister Tony Abbott.
Earlier on Monday, Xinhua news agency said a Chinese Ilyushin IL-76 aircraft spotted two "relatively big" floating objects and several smaller white ones dispersed over several kilometres.
Faint electronic "pings" also detected by Inmarsat suggested the jet flew for another six hours or so, though the initial analysis could do no better than place its final signal on one of two vast arcs, the north and south corridors.
Najib said Inmarsat had been performing further calculations on the data.
"Using a type of analysis never before used in an investigation of this sort, they have been able to shed more light on MH370's flight path," he said.
"Based on their new analysis, Inmarsat and the U.K. Air Accidents Investigation Branch 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."
Asked how Inmarsat experts had made the breakthrough, Chris McLaughlin, senior vice president for external affairs, said: "They tested (the earlier findings) against a number of known flights of other aircraft and came to the conclusion that only the southern route was possible."
The Inmarsat analysis has narrowed the search area "but it's still a big area that they have to search," said Stephen Wood, CEO of All Source Analysis, a satellite analytic firm.
BY NILUKSI KOSWANAGE AND SIVA GOVINDASAMY