At an emergency press conference, the Malaysian PM said that it is "with deep sadness and regret" that new data shows the flight "ended in the southern Indian Ocean".
After further tests of data British-based satellite company Inmarsat concluded that MH370 crashed into the sea, thousands of miles off course.
It wasn't close to any possible landing sites, said the PM, and was in the southern Indian Ocean to the west of Perth.
Investigators are still searching for any debris from wreckage and, crucially, the black box.
Razak said families had been informed of the latest developments by Malaysia Airlines.
He said: "The last two weeks have been heartbreaking. This news must be harder still."
There will be a further press conference tomorrow with more details, he added, from the press conference held in Kuala Lumpur.
The southern Indian Ocean is believed to be where the jet went down because Malaysian authorities have said pings sent by the Boeing 777-200 for several hours after it disappeared indicated that the plane ended up in one of two huge arcs: a northern corridor stretching from Malaysia to Central Asia, or a southern corridor that stretches towards Antarctica.
Malaysian authorities have not ruled out any possible explanation for what happened to the jet, but have said the evidence so far suggests it was deliberately turned back across Malaysia to the Strait of Malacca, with its communications systems disabled. They are unsure what happened next.
Authorities are considering the possibilities of hijacking, sabotage, terrorism or issues related to the mental health of the pilots or someone else on board.
Malaysia's police chief, Inspector General Khalid Abu Bakar, has reiterated that all the passengers had been cleared of suspicion.
But he said that the pilots and crew were still being investigated. He would not comment on whether investigators had recovered the files that were deleted a month earlier from the home flight simulator of the chief pilot.
In the US, Tony Blinken, President Barack Obama's deputy national security adviser, said on CNN: "There is no prevailing theory."
"Publicly or privately, we don't know," he said. "We're chasing down every theory."