The heir to the throne was informed of the tragedy in the Cairngorms, which appears to have begun when Rimon Than's party triggered the snowfall.
Squadron Leader Than, 33, was based at RAF Valley in North Wales, where the Duke is currently stationed, and died along with a female member of the RAF and a man from another party, neither of whom have yet been named.
The casualties were located after the alarm was raised at 12.30pm on Thursday, and airlifted to Aberdeen Royal Infirmary by search-and-rescue helicopter from RAF Lossiemouth. They were pronounced dead on arrival.
Sqn Ldr Than was a qualified doctor and a keen and experienced climber who was a member of the Army Mountaineering Association (AMA).
In December, he had been part of an AMA expedition to China, where his team conquered the previously unclimbed 18,504ft Wupingfeng mountain in Sichuan province.
The avalanche began as two groups of six climbers made their way up opposite sides of the Chalamain Gap, a deep, rocky cleft in the Cairngorms five miles south-east of Aviemore, not far from the Cairngorm ski slopes.
One group was part of a winter skills course run by outdoor training centre Glenmore Lodge, and the second comprised off-duty RAF personnel.
Mark Diggins co-ordinator of sportscotland's Avalanche Information Service (SAIS), said the avalanche had been on the north-west facing slope of the Chalamain Gap. "On one side it is heavy laden snow clear and the other side is bare rock and boulders. One side is 100% safe and the other side is not."
He said that when an avalanche involves people, it is likely to have been triggered by human activity.
Bob Kinnaird, principal of Glenmore Lodge, said "Our instructors are used to going out in these conditions. They are well trained and have the knowledge, skills and experience to look after groups.
"While it would be appropriate to go into the details of this incident today, I think time will show there was a very clear risk assessment and judgment call and this has just been a very tragic accident in relation to the Glenmore Lodge casualty.
"We have been doing training here for 65 years and this is the first fatality for at least 40 years for the centre."
Cairngorm Mountain Rescue Team leader Willie Anderson said: "These people were desperately unlucky. Sometimes these avalanches spontaneously happen, although sometimes they are caused by mountaineers."
After naming Sqn Ldr Than, police said all immediate next of kin had been informed, but that the families of the remaining victims had asked for some time to inform other friends and relatives, therefore no other details of those involved would be released for the time being.
Area Inspector Murdoch MacLeod said reports had been submitted to the procurator-fiscal: "It is important we pay tribute to work of the rescuers, who responded extremely quickly to the incident and located all three climbers in a short space of time."
Mr Diggins said: "I feel really sad about the seven deaths in avalanches in Scotland this year alone. We would put in a lot of work providing information. Many heed it.
"We can identify that in a four-month period we get between 250,000 and 400,000 people reading the avalanche reports, not just looking at the warnings. But we will never know how many people we have saved."