Japan's foreign ministry said the two were both men in their 60s, but declined to supply further details because their families had not given consent.
The two mountaineers had on Saturday scaled the 4,478- metre Matterhorn, whose pyramidal shape makes it one of the world's most recognisable mountains.
Swiss police said yesterday the body of one climber had been found but his climbing partner was still missing.
His body was later discovered, the Tokyo official said.
During their descent, the pair were caught off guard by bad weather and tried to return to the Solvay hut, which lies at 4,003 metres, but were unsuccessful, police in Valais canton said.
A Polish mountaineer who glimpsed one of the climbers on Sunday raised the alarm but the mountain rescue service was unable to reach the site until Monday due to bad weather.
The Matterhorn, which lies on the border of Switzerland and Italy, is one of the highest peaks in Europe and attracts around 3,000 climbers per year.
DNA tests recently confirmed that skeletal remains found in the Swiss Alps were those of two Japanese climbers who vanished in 1970. The remains were found after emerging from melting ice.
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