According to police in Switzerland, climbers discovered the human remains on Theodul Glacier in the Alps on July 12.
A picture released from authorities shows a single hiking boot and hiking equipment hanging from the side of the glacier.
Officials said the entire discovery was collected and taken a hospital for forensic examination.
The DNA from the recovery was a match for the hiker who went missing in 1986, police said.
The identity of the 38-year-old German mountaineer was not made public.
Deaths are not terribly uncommon in this part of the Alps, near the Matterhorn. An estimated 500 climbers diedon the Matterhorn between 1865 and 2011.
Melting glaciers are a major concern as the world grapples with global warming.
According to the United Nations, the Alps set a record for melt in 2022 due to heat waves, dust storms and rising CO2 levels.
Petteri Taalas, secretary-general of the World Meteorological Organization, said last year that "we have already lost the melting of the glaciers game."
Noting the seriousness of the issue, Taalas said the world's freshwater supplies could become limited. He added that extreme weather caused by greenhouse gas emission could continue until the 2060s despite successes made in fighting climate change.
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