The declaration brought an end to hope still held by families of the passengers of MH-370.
The flight, which disappeared on March 8 while en route from Kuala Lumpur to Beijing, crashed "far from any possible landing sites," said the prime minister.
A British satellite company, Inmarsat, and Britain's Air Accidents Investigation Branch were credited with providing new analysis of satellite data that the plane had crashed in the southern Indian Ocean.
"... with deep sadness and regret that I must inform you that according to this new data, MH-370's life ended in the southern Indian Ocean."
The prime minister said that a news conference on Tuesday would provide additional information.