But bad weather has forced the Air Accidents Investigation Branch (AAIB) to abandon hopes of pulling the plane to shore.
The light aircraft was carrying the 28-year-old footballer to his new Premier League team Cardiff City when it disappeared near the island of Guernsey on January 21, along with 59-year-old pilot David Ibbotson.
A shipwreck hunter hired by Sala’s family with the help of funds donated by football stars such as Lionel Messi found the plane wreckage on Sunday.
The AAIB who then took over the operation revealed on Monday that an unidentified body had been found at the site.
“In challenging conditions, the AAIB and its specialist contractors successfully recovered the body previously seen amidst the wreckage,” the Air Accidents Investigation Branch (AAIB) said Wednesday.
“The operation was carried out in as dignified a way as possible and the families were kept informed of progress.”
However, attempts to recover the aircraft during the underwater operation were unsuccessful.
“The weather forecast is poor for the foreseeable future and so the difficult decision was taken to bring the overall operation to a close,” the statement added.
It said that extensive video footage captured by a remotely operated vehicle is expected to “provide valuable evidence for our safety investigation,” adding that it intends to publish an interim report on the accident later this month.
The recovered body will be now be passed to the coroner for identification.
Sala was flying to join up with Cardiff from French team Nantes in what was the most expensive signing in the Welsh club’s history.
The plane, a Piper PA-46 Malibu, vanished from radar around 20 kilometres (12 miles) north of Guernsey, with pilot Ibbotson the only other person aboard.
After the official rescue team gave up their search, saying there was little chance of finding anyone alive, Sala’s family raised more than 370,000 euros ($422,000) in an online campaign to pay for a private hunt.
“Had that not happened, I don't think anybody would have searched for the plane,” said shipwreck hunter David Mearns, whose private company found the plane before calling in the AAIB.
The discovery of two seat cushions on the French coast last week revealed that the plane was broken, Mearns added.
Earlier this week Sala’s father, Horacio Sala, acknowledged that there was no prospect of finding his son alive.
“There's no longer any hope," he told Fox Sports.
“We hope the two bodies are inside (the plane). It's over, the only thing I hope now is that they find them.”