Steck, who was known as the “Swiss Machine”, died in an accident while acclimatising for an attempt on the mountain, without oxygen, by a new route.
The 40-year-old had won multiple awards and was known for his rapid ascents.
His body has been recovered from the mountain and flown to Kathmandu by helicopter.
On Wednesday Steck wrote on his Facebook page that he had a “quick day from Basecamp up to 7,000m and back” as he believed “active acclimatisation” was the most effective way of getting used to high altitude.
The climber reached Mount Everest’s summit without oxygen in 2012, and in 2015 climbed all 82 Alpine peaks over 4,000m (13,100ft) in 62 days.
Steck had returned to the world’s tallest mountain four years on from an altercation with sherpas which caused him to abandon an attempt to climb Everest and Lhotse.
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Ueli Steck set new standards in alpine climbing – setting a string of records for making breathtakingly quick solo ascents of classic routes.
He also played a big part in bringing the sport to a new audience through the epic films made of his exploits.
He was nicknamed the “Swiss machine” for his ruthlessly methodical approach and his ability to keep going even after pushing himself to the limits of human endurance.
In 2015 he climbed one of the world’s most famous walls, the North Face of the Eiger, in 2 hours 47 minutes – a time that would have been unthinkable to the early pioneers of the sport, who took days to complete it.
Source: http://www.bbc.com/news/