Based on analysis of ROV video footage, the AAIB investigators on board the vessel concluded that the object is wreckage from the missing Piper Malibu aircraft, registration N264DB.
Mearns said that both families have been notified by police.
Sky Sports reported Mearns' team had reduced their search area to just four square miles, with the plane eventually found 24 miles north of Guernsey.
He said a remote-controlled submarine deployed by the AAIB visually identified the wreckage, including the plane's registration number.
"I can not believe it".
He said the body was discovered using a remotely operated vehicle (ROV) belonging to the AAIB vessel Geo Ocean III.
He said that the reason why it was spotted so quickly was that the plane lay very close to the "datum position", the last known coordinates that they were guided by.
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The wreckage was found hours after the search started near the Channel Island Guernsey by a private rescue operation hired by Sala's family.
The privately-funded operation on behalf of the Sala family was made possible after a campaign raised more than £260,000 to pay for it.
An official search was called off after three days when rescuers said there was little chance anyone aboard the single-engine aircraft had survived.
"They went through various stages of identification through the course of today, and David Mearns confirmed to me that they have now positively identified the wreckage as that of the plane that had been carrying the Argentinian footballer".
In a statement, the the AAIB added: "We intend to publish an interim report within one month of the accident occurring".
The 28-year-old soccer player was on his way to Cardiff after being signed by the Welsh capital's Premier League team when the aircraft vanished.
Nantes' Emiliano Sala in action in a FC Nantes v OGC Nice in March 2-017.