Sala, 28, had been flying from his previous club Nantes in western France to Wales on Jan. 21 to make his debut for the Premier League team when the single-engined Piper Malibu aircraft disappeared over the sea.
Wreckage was found on Sunday following a privately-funded underwater search and a body recovered on Wednesday and taken to southern England.
"The body brought to Portland Port today... has been formally identified by HM Coroner for Dorset as that of professional footballer Emiliano Sala," the police statement said.
"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. Our thoughts remain with them at this difficult time."
Cardiff posted the statement on their website under a picture of the player.
"We offer our most heartfelt sympathies and condolences to the family of Emiliano. He and David will forever remain in our thoughts," the Welsh club said.
Sala had agreed to join relegation-threatened Cardiff for a club-record fee of 15 million pounds ($19.43 million) from French Ligue 1 club Nantes.
Police said an investigation into the circumstances of the death was continuing.
Efforts to recover the aircraft wreckage have so far been unsuccessful due to poor weather conditions.
The plane had been cruising at 5,000 feet (1,525 m) when the pilot requested to descend to a lower altitude on passing Guernsey. It then lost radar contact at 2,300 feet.
Argentine newspaper Clarin last month published a voice message that Sala, who had played in France since 2012 and scored 12 goals for Nantes this season, apparently sent to friends while in the air.
"We're up in the plane and it seems it's about to crash," said the message, which Clarin said was verified by Sala's father, Horacio Sala.
"If you have not heard anything from me in an hour and a half, I don't know if they're going to send someone to find me, because, you know, they're not going to be able to," the message said. "Dad. I'm really scared."
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