An aircraft carrying the Cardiff City player, flown by David Ibbotson, crashed on 21 January en route from Nantes to Cardiff.
A body was recovered from the sea north of Guernsey and formally identified by the Dorset coroner after being brought to the UK.
Cardiff City, for which Sala had recently signed for a club record £15m, said: “We offer our most heartfelt sympathies and condolences to the family of Emiliano. He and David will for ever remain in our thoughts.”
Manchester City’s Sergio Agüero, a fellow Argentinian, tweeted: “Rest in peace, Emiliano. My condolences to his friends and family.”
Argentina’s president, Mauricio Macri, who had joined calls for the search for the pair to be resumed after it was called off, also sent his condolences to Sala’s family on Twitter, saying: “We are with you.”
Mesut Özil of Arsenal wrote: “No words to describe how sad this is. Thoughts and prayers go out to his family and also to the family of the pilot.”
Manchester City’s Benjamin Mendy tweeted an image of Sala, while the Paris Saint-Germain forward Kylian Mbappé wrote simply: “RIP Emi.”
The Everton player Oumar Niasse, who is on loan at Cardiff City, tweeted: “RIP EmilianoSala1 for ever in our thoughts”.
David Mearns, the shipwreck expert who led a private search for the plane, tweeted: “Rest in peace Emiliano. I was glad to provide some small comfort to … the whole Sala family during the past two weeks, but my heart goes out to the family and friends of David Ibbotson, whose loss is the same.”
Dorset police said: “The body brought to Portland port has been formally identified by HM coroner for Dorset as that of professional footballer Emiliano Sala.
“The families of Mr Sala and the pilot David Ibbotson have been updated with this news and will continue to be supported by specially trained family liaison officers.”
The wreckage of the Piper Malibu N264DB that was carrying the two men was found in the sea off the Channel Islands on Sunday, and investigators said shortly afterwards they had seen a body inside.
Efforts then began to recover and identify the body, though they were made more difficult by poor weather conditions.
Sala had recently been signed by Cardiff City from the French club Nantes. He was returning to south Wales from the French city, which he had visited to say goodbye to old friends and teammates, when the crash occurred.
Dorset police said the coroner would continue to investigate the circumstances of Sala’s death, supported by its officers. The Air Accidents Investigation Branch also said it had decided not to continue efforts to raise the plane, which it had surveyed using a remotely operated vehicle.
“Unfortunately, attempts to recover the aircraft wreckage were unsuccessful before poor weather conditions forced us to return the ROV to the ship,” the AAIB said.
“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 AAIB said the operation to recover Sala’s body was “carried out in as dignified a way as possible” in challenging conditions.
While it could not raise the plane, the body said “extensive video record captured by the ROV is expected to provide valuable evidence for our safety investigation”. Investigators said they would produce an interim report on the crash by 21 February.
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