Sergeant Martin Spooner and Corporal Carl Bougard were rescued 19,000ft up Mount McKinley, Alaska, by a helicopter during a brief break in appalling weather and against a 40mph gale.
Despite enduring days without food or radio contact, the soldiers, both aged 35, were said to be in good spirits. Sgt Spooner - who fell 300ft down a snow chute - injured his ankle. He is also suffering from minor frostbite after wind-chill temperatures dropped to -62C.
Cpl Bougard, who volunteered to stay with Sgt Spooner after the fall, was suffering from the effects of cold and exhaustion.
The two men came out alive because of the snowhole they had dug for shelter, their waterproof sleeping bags, down jackets and a small stove to melt drinking water.
As the men recovered in hospital, the Army announced it would launch an inquiry into the ill-fated charity expedition to scale the mountain.
Lieutenant Colonel Mark Rayner said: "We would stress that this is not a witch-hunt. It is purely to find out exactly what went wrong. I think it is evident from the way in which the expedition members conducted themselves that this was a very well-planned expedition."
Dr Miles Nelson, who has been treating Sgt Spooner and Cpl Bougard, said Sgt Spooner had been released from hospital: "They are already talking about climbing the mountain again. Normal people would have perished in the conditions they experienced but their intelligence saved them and they are lucky to be alive."
Speaking from her home in Canterbury, Kent, Paula Wanstall, Cpl Bougard's girlfriend, said: "These last few days have been absolutely terrible. A real nightmare. I'm obviously over the moon to learn that he has been rescued and that he seems to be in good health and I just can't wait to see him."
The men were part of a nine-strong British expedition aiming to be the first to climb the mountain, then descend and reach sea level in Alaska by canoeing to the coast through treacherous rapids.
They were raising money for a Barnardo's project to enable youngsters to take part in leisure and sporting activities.
The team members were experienced climbers, but got into difficulties when three of the men - Sgt Spooner, Lance Corporal Steve Brown and Captain Phil Whitfield, 23 - fell 300ft down a snow-filled gully, known as the Orient Express, while roped together.
The team's leader, Captain Justin Featherstone, 28, and Cpl Bougard stayed with Sgt Spooner and Lce Cpl Brown, while Capt Whitfield and another climber, Sgt Johnny Johnston, 33, descended to raise the alarm.
Lce Cpl Brown and Capt Featherstone attempted a descent late on Friday, but fell a further 2,000ft. Capt Featherstone broke both his legs in that fall, but rescuers were able to drag him back to the camp.
This left Sgt Spooner, a married man with two children, and Cpl Bougard on the mountain. The weather cleared enough for emergency rations to be dropped to them a few hours before their rescue.
The final recovery took place at 11.55am GMT when the rescue crew from the United States National Parks Service made the most of a short midsummer night and the smallest of gaps in dense cloud and driving snow.
A Ministry of Defence spokesman said: "The helicopter can only spend a few minutes before it has to refuel, so it is clearly a great challenge for any air crew."Reuse content