Sala, 28, was on board the Piper Malibu plane with David Ibbotson, 59, the pilot, when it disappeared from radar near Guernsey on January 21.
The aircraft remains 67 metres underwater 21 miles off the coast of Guernsey in the English Channel as poor weather conditions stopped efforts to recover it.
The AAIB said one of the occupants was visible amid the remains of the plane and have now confirmed that a recovery has been successful.
It was carried out in "as dignified a way as possible" and the men's families were kept updated throughout, it said.
The AAIB also confirmed that the body will be taken to Portland, Dorset where it will be passed onto the county coroner.
Weather conditions have been so poor that the AAIB has called off any further attempts to recover the aircraft itself.
There is no timetable for identification of the recovered body, and an interim report is expected to be published by the AAIB within the month.
A statement from the AIBB read: "Following extensive visual examination of the accident site using the remotely operated vehicle (ROV), it was chose to attempt recovery operations".
It is understood that Cardiff received a letter from Nantes on Tuesday, in which the French Ligue 1 club threatened to take legal action if the first scheduled payment of the fee is not made within 10 days.
'Although it was not possible to recover the aircraft, the extensive video record captured by the ROV is expected to provide valuable evidence for our safety investigation.
Earlier today Nantes reportedly demanded the £15 million transfer payment from Cardiff City.