West, who suffered frost bite to one cheek during the expedition in often atrocious conditions of heavier than expected snow, 50mph winds and -50C temperatures, added: "Harry also massively helped me out when I was struggling with my skis at first. He was a great guy."
He also told how the Prince joined in some exuberant celebrations when they reached the South Pole on December 13.
Two Australians stripped naked, while Harry and the others sipped Champagne from bottles wedged in one of the artificial limbs of Duncan Slater, a Sergeant in the RAF regiment injured in Afghanistan in 2009.
"Two of the Aussie guys stripped naked and ran round the pole but most of us, Harry included, just went on a two-day bender with the Icelandic truck drivers who had brought some lethal home brew with them," West said.
"There was a lot of liqueur drunk.We all drank champagne out of Duncan's favourite prosthetic legs."
Asked what was Harry's greatest talent, he replied: "Well he told some eye-wateringly rude jokes which for a non-soldier like me was pretty shocking."
Sgt Slater, 34, from Diss, Norfolk, said Harry was brilliant at keeping up the morale of the 12 wounded service personnel and the support workers by arranging cricket games in the snow or competitions to build the most elaborate latrines. "It was always him who was instigating it. There were so many wind-ups," he said.
"He would kind of spread himself quite thinly to be honest. He would spend time with each team member. He would make sure he mixed with everyone."
Sgt Slater, who insisted his injuries paled into signifance compared to the difficulties of blind American team member Ivan Castro, will join the British team of three men and one woman, Major Kate Philp, in running the London Marathon on April 13.
"For some the journey may be more of a challenge and it falls to all of us to help them where we can, be that in training, employment, sport or even adventure."
Harry, who is patron of the marathon as well as Walking With The Wounded, will not compete but is expected to present the medals.
The young prince spoke out about the brave challengers, who spent almost two weeks pulling sleds across the frozen wastes of Antarctica to reach the South Pole, and used his speech to both praise the wounded and to emphasise the importance of supporting all personnel returning home from war.
"These injured men and women are not seeking pity," he said.
"They just simply want to be treated in the same way that they were before they were injured."
Harry, who last week announced he is leaving his role as an Apache helicopter pilot to begin a new job with the army based in London, added: "For some the journey may be more of a challenge and it falls to all of us to help them where we can, be that in training, employment, sport or even adventure.
"So if anybody out there has the ability or resources to give these guys and girls a stepping stone back into employment then please do, you certainly won't regret it."
During the trek, which saw them face extreme weather conditions every day, Harry said: "Every single person who takes part in this challenge is extraordinary.
"The fact these guys have made it to this point is extraordinary and I count myself incredibly lucky to be part of it."
Before the speech the fourth-in-line to the throne was reunited with his British team-mates including Duncan Slater, Ibrar Ali, Kate Philp, Guy Disney, guide Conrad Dickinson and mentor Richard Eyre.
Meanwhile, Harry has praised fellow South Pole adventurers Ben Saunders and Tarka L'Herpiniere, who are currently on their way back home from the same challenge that Captain Scott took on back in 1912.
The pair received their royal message on January 17, the day Captain Scott and his party reached the South Pole in 1912 - an anniversary they commemorated while on the ice.