The wing section, known as a flaperon, had been examined in France by international aviation experts.
French authorities launched searches on and around Reunion for more debris but none was found.
MH370 flight carrying 239 people veered off its course from Kuala Lumpur to Beijing in March 2014.
The Malaysian government had previously said it believed that the flaperon belonged to MH370.
French investigators had until now been more cautious on the provenance of the debris.
However, on September 3 they said a technician from Airbus Defense and Space (ADS-SAU) in Spain, which had made the part for Boeing, had formally identified one of three numbers found on the flaperon as being the same as the serial number on MH370.
The magistrate charged with conducting the investigation and an aviation expert had gone to ADS-SAU headquarters on September 3.
The families of those aboard – who were mostly Chinese – have been angered by the apparent discrepancies in statements by French and Malaysian officials, and have accused the authorities of hiding the truth.
The Australian Transport Safety Bureau (ATSB) has been co-ordinating the deep-sea search in the southern Indian Ocean, where the plane is believed to have gone down, thousands of miles east of Reunion.
Australia’s PM Tony Abbott has said that the search would continue as “we owe it to the hundreds of millions of people who use our skies”.
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