Mr Razak said international experts examining the debris in France had “conclusively confirmed” it was from the aircraft.
The Malaysia Airlines plane carrying 239 people veered off course from Kuala Lumpur to Beijing in March 2014.
The debris was examined at an aeronautical test centre near Toulouse.
It was found on the remote French Indian Ocean island of Reunion a week ago.
In a statement, Mr Razak said the “the burden and uncertainty faced by the families” in the 515 days since the aircraft disappeared had been “unspeakable”.
“We now have physical evidence that flight MH370 tragically ended in the southern Indian Ocean,” he added.