The Geo Ocean III specialist search vessel docked in Portland
Remotely operated vehicles in "challenging conditions" were used to pull the body out of the water "in as dignified a way as possible", according to the Air Accidents Investigation Branch (AAIB).
Images show an ambulance bringing the body from a ship into land at Dorset this morning, and it has now been brought on to land.
It has not been confirmed whether the body is that of Sala or Mr Ibbotson.
Dorset Police released a statement which said: "This morning, Thursday 7 February 2019, the body was brought to Portland Port, Dorset, as this is the nearest part of the British mainland to where the plane was located.
"The arrival of the body into Dorset has been reported to the Coroner for Dorset. The Coroner will investigate the circumstances of this death supported by Dorset Police. A post-mortem examination will be held in due course."
Katerina Vittozzi, in Portland for Sky News, said: "The AAIB has gathered a huge amount of video evidence, so they do have enough to start to piece together what happened in the final moments before the plane came down.
"The vessel only got into the harbour after 9am, though the mission happened overnight. They have taken their time over time.
"No formal identification has been made public. This will happen before the coroner will announce if they want to open an inquest."
The body is to go to the Isle of Portland in order to be passed into the care of the Dorset coroner, an AAIB spokesman said.
Poor weather conditions stopped efforts to recover the aircraft, which remains 67 metres underwater, 21 miles off the coast of Guernsey in the English Channel.
An AAIB spokesman said bad weather was forecast "for the foreseeable future and so the difficult decision was taken to bring the overall operation to a close".
The investigators will publish their interim report within a month and footage captured of the wreckage is expected to provide "valuable evidence", it added.
The plane was discovered on Sunday by marine recovery specialists who were hired thanks to a crowdfunding appeal launched after the official search was called off.
Sala had signed for Cardiff City from French club Nantes in a £15m deal two days before the plane disappeared on 21 January.
Sky sources say Nantes have now started legal action against Cardiff, asking for the first payment of the transfer fee, which is understood to be more than £5m.
Cardiff have not yet paid any of the fee, a record for the club, for the Argentinian striker and privately believe questions first need answering about the ownership of the Piper Malibu aircraft and other issues.
The plane, which was travelling to Cardiff from Nantes, had requested to descend before it lost contact with Jersey air traffic control.
An official search operation was called off on 24 January after Guernsey's harbour master David Barker said the chances of survival following such a long period were "extremely remote".
The remains of the aircraft were tracked down by a team co-ordinated by ocean scientist David Mearns, who has located some of the most elusive wrecks in the world.
Mr Mearns - known as the "Shipwreck Hunter" - and his team located the aircraft within two hours of commencing their search.
Look at who the owners of the owners are, and I bet you'll find he was a pawn.
R.C.