Sala's body was recovered from the English Channel and formally identified on Thursday evening, nearly three weeks after his plane crashed en route to Cardiff - whom he joined for a club-record €17 million.
The light aircraft carrying Cardiff City's £15m January signing disappeared almost two weeks ago as he was flying to Wales to meet up with his new teammates, when the plane carrying him and pilot David Ibbotson lost contract with air traffic control. "Our thoughts remain with them all", police said.
Dorset Police said they would continue to support the coroner's investigation into the circumstances of the crash.
Cardiff City face a potential transfer ban if they continue to withhold the first installment of Emiliano Sala's £15 million fee.
Wreckage from the plane was located Sunday after Sala's family raised funds for a private search by American-born shipwreck-hunting specialist David Mearns that was conducted in conjunction with British air accident investigators.
He tweeted: "Rest in Peace Emiliano".
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In the wake of his death, the sporting world has paid tribute to the 28-year-old.
Football governing bodies Fifa, Uefa and the Football Association of Wales, along with Argentina's president Mauricio Macri all paid tribute to Sala.
"We offer our most heartfelt sympathies and condolences to the family of Emiliano", Cardiff City said in a statement on Thursday.
A recovery operation was then launched following consultation with the families of Sala and Ibbotson, and the police.
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.
Last weekend, Cardiff commemorated Sala during their match in the Premier League.
Remotely operated Vehicles (ROVs) were used in tough conditions to pull the body out of the water in a "dignified" way, the Air Accidents Investigation Branch (AAIB) said.
The whereabouts of Mr Ibbotson remain unknown, although the pilot is also presumed dead.