Charity LBT Global said that, while formal identification has not yet taken place, the remains were found with the 19-year-old’s clothes and possessions near his last known location.
Members of a mountain rescue team from the Spanish Civil Guard discovered the body near the village of Masca on Monday.
The force said Mr Slater, from Oswaldtwistle, Lancashire, could have fallen in the steep and inaccessible area where he was discovered.
It released video footage of rescuers climbing rock faces and battling through scrub as they carried out the search.
Part of the clip shows two members of the search team being winched out of the area by helicopter after the body had been found and recovered.
Mr Slater had attended the NRG music festival with two friends before his disappearance, and his last known location was the Rural de Teno Park in the north of the Canary Island, which was about an 11-hour walk from his accommodation.
He had travelled to an Airbnb in Masca after a night out, but the two men said to have rented the property were later ruled “not relevant” to the case.
LBT Global, which supports the families of British people missing overseas, said: “LBT Global is saddened to announce that a body found in Tenerife does look to be that of Jay Slater.
“It is understood the body was found close to the site of his mobile phone’s last location.
“Although formal identification is yet to be carried out, the body was found with Mr Slater’s possessions and clothes.
“A post-mortem examination and forensic inquiries will follow.
“LBT Global are supporting the family at this distressing time and ask for everyone to afford them space and privacy to come to terms with the news.”
His family endured conspiracy theories and “awful comments” being posted online during the search for the apprentice bricklayer, but supporters had raised £50,000 to help fund the hunt for the teenager.
Tenerife’s Guardia Civil said on Monday that officers are waiting for the results of a post-mortem examination to confirm that Mr Slater died as a result of an accident.
Spanish police called off the search for the apprentice bricklayer at the end of June after helicopters, drones and search dogs were deployed to find him.
But in its statement on Monday, the force said teams had not stopped searching every day.
“The discovery was possible thanks to the incessant and discreet search carried out by the Civil Guard during these 29 days, in which the natural space was preserved so that it would not be filled with onlookers,” its statement read.