Sala, 28, was travelling from France to join up with his new club, Premier League side Cardiff City, in a light aircraft manned by David Ibbotson on January 21 when it disappeared close to the Channel Islands.
Tributes were paid to the striker on both sides of the Channel over the weekend as hopes faded he would be found alive, and Britain's Air Accidents Investigation Branch (AAIB) on Sunday told AFP the plane's wreckage had been discovered.
"I can confirm it has been found," a spokesperson said, adding a statement would be issued on Monday.
Sala's father Horacio spoke of his shock from his home in Progresso, Argentina, telling Cronica TV: "I can't believe it. It's a bad dream."
Horacio was the only member of the Sala family to stay behind in Argentina as the others rushed to France to try to help with the search.
"I talk to them every day. But since I don't have WhatsApp it's expensive to call them or for them to call me. But anyway, they kept saying days were going by, and that there had been zero word on Emiliano, or on the plane," he said.
Suspected debris from the plane washed up on the Normandy coastline in France last Wednesday.
Sala was travelling in the Piper PA-46 Malibu plane after transferring from French team Nantes in a 17 million euro ($19.3 million) move -- a record deal for the Welsh team.
It vanished from radar around 20 kilometres (12 miles) north of Guernsey, with pilot Ibbotson the only other person aboard.
David Mearns, whose private company, Blue Water Recoveries, was hired by Sala's family to search for the plane, said on Twitter that the wreckage was spotted early Sunday.
"There's a substantial amount of wreckage on the seabed," he wrote, adding: "This is about the best result we could have hoped for the families."
Top footballers were among more than 4,500 contributors to a crowdfunding page that raised over 300,000 euros ($343,000) to look for the wreckage.
Speaking after Cardiff's match against Bournemouth on Saturday, manager Neil Warnock said Sala would have been "really proud" of the team after they won 2-0 in their first home match since the plane vanished.
Programme notes, penned by owner Vincent Tan and the rest of the Bluebirds' board, said events had shaken "Cardiff City to its very core" and that they were now playing for Sala and pilot Ibbotson.
There were a series of heartfelt tributes before kick-off, with Sala's photograph appearing on the front cover of the matchday programme and the two captains laid floral tributes on the halfway line before what the club called a "silent reflection".
Sala's name, in the Argentina colours, was also spelled out behind one of the goals as supporters held cards aloft.
burs-je/amu