The trip has taken four years to plan and saw 80 applicants apply, with only a dozen reservists and regular soldiers making the cut.
The island, which is also the fifth-largest in the world, is a place where the British Army has never previously sent its personnel.
The Arctic Mountaineer Expedition has taken four years to plan and saw 80 applicants apply, with only a dozen reservists and regular soldiers making the cut.
Before departing, the Arctic Mountaineer team had to make sure their equipment was ready.
Sergeant Ross Denver, Royal Army Physical Training Corps, said they were: "Fitting boots to skis, making sure the skins are working - and they're actually the right ones for the skis, and then any other sort of kit stuff like getting spares together and making sure we're not all taking two of something that we don't need."
The team of 12 will spend three weeks on Expedition Arctic Mountaineer battling temperatures lower than -20°c.
Frostbite, hypothermia, and fatigue are high on the list of Baffin Island hazards.
If the team encounters an accident or emergency, the nearest medical facility will be 12 hours away.
Captain Sarah Bass, 355 Medical Evacuation Regiment, has been preparing for eventualities: "I've had to come up with a whole medical kit that I need to take - that covers everything from if someone breaks their legs to really simple stuff that people are going to get like chilblains or cold sores, things like that, so there's been a lot of planning."
Lieutenant Colonel Terry Denton, Royal Electrical Mechanical Engineers, added:
"There's some really specific things about operating in the Arctic that make it a little bit different equipment-wise... you really have to consider some of these issues."
"It shouldn't be too much of a problem; we're quite far away from the coast where the bears tend to be.
"But at this time of year, as they start to move around, then there is a threat from bears."
Maj Davies continued: "This provides the 12 of us an opportunity to go further afield, have broader experiences, work through different problems, different mountaineering terrain so that when we come back and we lead other soldiers in the mountains in Europe and in Scotland, we've got a broader experience base to work from."