DNA tests confirmed that the body is that of a 38-year-old man who went missing in September 1986.
Valais Cantonal Police said the remains were discovered alongside various pieces of equipment on the Theodul Glacier in Zermatt, near the famous Matterhorn mountain.
The remains were found by mountaineers who spotted a lone hiking boot and crampons sticking out of the ice on 12 July.
The body was later transported to a nearby hospital for analysis before genetic tests confirmed the man's identity.
His identity has not been made public by the regional police.
Increasing glacier melt, which many scientists blame on global warming, has spurred a recent increase in discoveries of the remains of hikers, skiers and other Alpinists who went missing decades ago.
Swiss climatologists and other experts say the country's glaciers have been melting at accelerated rates in recent years, attributing it in part to climate change caused by human activity.
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