"We have a positive ID ... Fingerprinting confirms that the body belongs to Jay Slater and the death was due to multiple traumas compatible with a fall in the mountainous area," a court spokesperson said.
Earlier, the same spokesperson said it would take some days before autopsy results were available.
Slater's mother Debbie issued a statement through the British overseas missing persons charity, LBT Global, acknowledging the "worst news".
"I just can't believe this could happen to my beautiful boy," the statement read.
"Our hearts are broken."
The body was found on Monday morning by a Civil Guard mountain rescue group.
Slater, 19, went missing on June 17 and his phone was last traced to the Masca ravine in a remote national park on the Canary Islands archipelago.
The remains were found with Slater's possessions and clothes and it is understood it was discovered close to the site of his mobile phone's last location, LBT Global said on Monday.
Matthew Searle, chief executive of LBT Global which has issued several statements on behalf of the family, said it would help repatriate Slater's body and belongings and make funeral arrangements.
"There will, of course, be many more hurdles for the family to face in the coming days and we will work with them to make this horrific time as easy as possible," he said.
