"We offer our most heartfelt sympathies and condolences to the family of Emiliano", Cardiff City said in a statement on Thursday.
Despite Sala's importance to Nantes, he was keen to move on, and club president Waldemar Kita was keen to cash in on a player whose contract was due to expire in 2020.
Despite that, Sala never played for his country and remained little known back in his homeland - an article on the website of popular sports daily Ole last month carried a headline: "Who is Emiliano Sala?".
Earlier this week, the footballer's father, Horacio Sala, acknowledged that there was no prospect of finding his son alive.
Chelsea defender Antonio Rudiger wrote: "Heartbreaking to hear the news about Emiliano Sala. My condolences to his friends and family".
Gary Lineker tweeted: "How terribly sad". "Our thoughts and prayers are with you and your family".
He is yet to be found.
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 investigation to find the plane was initially called off after three days, but Sala's family raised the funds to keep the search alive, with thanks to donations from worldwide football community.
Noted shipwreck hunter David Mearns located the wreckage using sonar after scouring sections of the English Channel.
The body was glimpsed in underwater footage taken of the wreckage and recovered by remotely operated vehicles (or ROVs) on Wednesday.
"Unfortunately, attempts to recover the aircraft wreckage were unsuccessful before poor weather conditions forced us to return the ROV to the ship".
"The weather forecast is poor for the foreseeable future and so the hard decision was taken to bring the overall operation to a close".
Sala, 28, had just completed a club-record £15million transfer to Cardiff and had not made an appearance for the club.