The team's cosy camp

They radioed Expedition Base Manager John Perrins, who is in Resolute Bay in the high Arctic, with the news of their whereabouts.

They will now wait for their families and sponsors, who are already on their way, to see them complete the final feat.

And what a feat it has been. To complete the Grand Slam, an explorer must walk to the North and South geographical poles, reach the North and South magnetic poles, and climb the highest summit in each of the seven continents, including Mount Everest and Mount Kilimanjaro.

In their journey to reach the North Pole, Mr Hempleman-Adams and Mr Gjeldnes have spent 55 days trekking across 600 miles of snow and ice and have slept nights out in the frozen expanse - with just each other for company.

Rune Gjeldnes cooks dinner

Yet for Mr Hempleman-Adams, who is now making his third attempt to reach the North Pole, the only way was up.

"It was amazing, " he said. "We were having breakfast and we heard a jet go over. We're here freezing, having dehydrated food, while they're up there having their champagne and lobster.

"And do you know where I wanted to be? Here. Because I want to get to the North Pole."

There were, of course, some hair-raising moments. Open water, as wide as a river, is a rare sight in the Arctic and one which poses the biggest danger to the expedition. The Anglo-Norwegian team spent two days trying to find a way across the icy waves.

Claire Hempleman-Adams has arrived to see her husband make it to the top

Mr Hempleman-Adams's wife, Claire, has now arrived at Resolute Bay, with their daughter, Alicia, after a two-day journey from Britain to meet her husband. She is eager to get a taste of what her husband has been experiencing.

"There wasn't much to see from the plane, expect a huge white mass. It'll be really good to actually get down on the ground and see what it's like from their point of view," Mrs Hempleman-Adams said.

Everything is now set for a party at the top of the world as Mr Hempleman-Adams and Mr Gjeldnes set off on Thursday to plant their flags on the North Pole and end the challenge of a lifetime.