Tom Riddelsdell, 27, a software developer from the Isle of Wight, and Matthew Beals, a 28-year-old financial analyst from Preston, were rescued after a 16-hour ordeal on the mountains.
They had been in a party of four but the two other climbers had decided to do a different route and managed to get safely off the hill to raise the alarm at about 6.30pm on Wednesday.
They had been climbing on the Stag Rocks, a well-known site for mountaineers in the Cairngorms.
However, they decided to abandon the climb as conditions worsened. One of their ropes got stuck during their descent and Mr Beals had to go back up to dislodge it, delaying them.
By the time they reached the bottom it was dark and they had to dig a snow hole for shelter but it collapsed on them. They were soaked through but managed to squeeze themselves into a bivvy bag.
Mr Beals said: "It was fine when we were digging the hole but when we got into it and into the bivvy bag, that was a bit scary. It was dripping wet and we could hear the winds howling."
Mr Riddelsdell added: "It was pitch black and we couldn't see the gully. We didn't want to get lost on the plateau so we decided to dig in."
Cairngorm, RAF Lossiemouth and Braemar mountain rescue teams began the search at first light on Thursday, supported by a search and rescue helicopter from Lossiemouth.
They found them making their own way down at around 10.30am.
Mr Riddelsdell said: "We couldn't believe the efforts of the rescuers. We massively appreciate it. They are heroes and legends."
Willie Anderson, Cairngorm Mountain Rescue Team leader, said the bivvy bag had probably saved them from hypothermia. He said that without the bag "it would have been a different story".