Susan McLean, 61, was last seen in Aberfeldy on 17 May.
The remains were found by a volunteer searchers in a wooded area near the town on Saturday.
Police Scotland said the death was being treated as "unexplained". Ms McLean's family have been informed and a formal identification will take place later.
The last suspected sighting of the tourist was on CCTV footage on Crieff Road outside the grounds of Moness Resort on the evening of her disappearance.
She had been on a two-week tour of Scotland with her family.
Supt Graeme Murdoch, of Police Scotland, said: "On Saturday 15 August, human remains were found during a volunteer search in dense undergrowth in a wooded area near Aberfeldy.
"A police investigation has been ongoing following the disappearance of Susan McLean.
"The family has been informed of the discovery and formal identification will take place in due course.
"The death is being treated as unexplained and as with all sudden deaths a report will be submitted to the procurator fiscal."
He added: "We would like to thank members of the public who have given up their time and continued to assist the search."
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