Australian PM Tony Abbott has said the "baffling mystery" of Flight MH370 is closer to being solved, after Malaysia said a fragment found in Reunion was part of the missing plane.
PM Najib Razak said experts examining the debris in France had "conclusively confirmed" it was from the aircraft.
However investigators have stopped short of confirming the link, saying only that it is highly likely.
Australia says it remains confident it is searching in the right area.
The Malaysia Airlines plane was travelling from Kuala Lumpur to Beijing on 8 March 2014 when it vanished from radar. It had 239 people on board.
The debris found on the remote French Indian Ocean island a week ago - a wing part known as a flaperon - was the first possible trace, and was taken to Toulouse for testing.
On Thursday, Mr Najib held a news conference in Kuala Lumpur to announce that investigators had "conclusively confirmed that the aircraft debris found on Reunion Island is indeed from MH370".
This would "at least bring certainty to the families", he said.
French prosecutor Serge Mackowiak said only there were "very strong indications" this was the case, and that confirmation would only come after further tests.
The BBC's Hugh Schofield in Paris said Mr Mackowiak's caution did not suggest he had doubts, but that he was exercising legal caution.
Mr Abbott later told reporters that the find "does seem to indicate the plane did come down more or less where we thought it did".
"It suggests that for the first time we may be a little bit closer to solving this baffling mystery," he said.
But he said the Australian-led search for the body of the plane would continue as "we owe it to the hundreds of millions of people who use our skies".
The Australian Transport Safety Bureau (ATSB) has been co-ordinating the deep-sea hunt in the southern Indian Ocean, where the plane is believed to have gone down, thousands of miles from Reunion.
MH370: Reunion debris is from missing plane, says Najib
Part of the aircraft wing found on Reunion Island is from the missing MH370 plane, Malaysian Prime Minister Najib Razak has confirmed.
Mr Najib said experts examining the debris in France had "conclusively confirmed" it was from the aircraft.
But the investigators have stopped short of confirming the link, saying only that it is highly likely.
The Malaysia Airlines plane carrying 239 people veered off course from Kuala Lumpur to Beijing in March 2014.
The debris was found on the remote French Indian Ocean island a week ago and was taken to Toulouse for testing.
The plane is long believed to have crashed into the southern Indian - though no evidence had been found despite a massive search operation.
"It is with a very heavy heart that I must tell you that an international team of experts has conclusively confirmed that the aircraft debris [...] is indeed MH370," Mr Najib told reporters in Kuala Lumpur.
"We now have physical evidence that [...] flight MH370 tragically ended in the southern Indian Ocean," he added.
Mr Najib said he hoped the discovery "will at least bring certainty to the families" of the victims, saying the burden they had faced was "unspeakable".
'Very strong indications'
French prosecutor Serge Mackowiak later confirmed the wing fragment, known as a flaperon, was from a Boeing 777 - the same make and model as the missing Malaysian airliner.
He said initial tests showed there were "very strong indications" that it was from flight MH370. But he said confirmation would only come after further tests on the fragment, which would begin on Thursday.
"[Investigators] will try to do it as soon as possible in order to provide total and reliable information to the family of victims, who are on our minds at the moment," Mr Mackowiak added.