Tom Billings, 22, from Oxford, was spending eight weeks travelling in North America when he was last seen in Vancouver in November 2013. He was reported missing a week later after he failed to return to his accommodation.
See also: British tourist goes missing in Vancouver
See also: Forest hiker 'on the verge of dying' rescued after five days
A large-scale search operation was launched for Mr Billings, who police believed was trekking in the North Shore mountains and got lost or injured, but he was never found.
Last month a hiker on Cypress Mountain in West Vancouver spotted the Briton's remains and he has since been identified through DNA, Vancouver Police said.
Foul play is not suspected and the coroner's service is investigating the death, the force said.
Mr Billings' father Martin issued an emotional appeal for help to find his son during a police press conference in Vancouver in December 2013.
He said he last exchanged emails with his Tom, who had recently graduated from university, when he was in was in Seattle in the US.
"I think the most likely thing is he has got in trouble on the mountain," Mr Billings said at the time.
"The things that have gone through my mind are in many ways too horrible to mention, I cannot deny that."
Mr Billings said his son had been using a "window" before starting postgraduate research to explore North America by hitch-hiking, travelling by bus and using "couch surfing" - staying with hosts he had met through the internet - as accommodation.
In a statement issued by police, Tom's parents thanked the public for "the support and assistance in the search to find their son" and the rescue teams involved in the search operation.