He said Malaysia Airlines had told the families of the 239 people on board.
Earlier the BBC saw a text message sent to families saying it had to be assumed “beyond reasonable doubt” that the plane was lost and there were no survivors.
Flight MH370 went missing after taking off on 8 March.
The announcement by PM Najib Razak came on the fifth day of an international search effort in the southern Indian Ocean.
Based on new analysis, the UK’s Air Accidents Investigation Branch and Inmarsat, the UK company that provided satellite data, “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,” he 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.”