PUBLISHED: 15:31 GMT, 24 March 2014 | UPDATED: 22:28 GMT, 24 March 2014
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.
Najib Razak: "It is with deep sadness and regret, that according to this new data, flight MH370 ended in the southern Indian Ocean.
Flight MH370 'crashed in south Indian Ocean'
- Malaysia PM