Sgt Slater, who lost both his legs below the knee after the vehicle he was travelling in was hit by an explosive device in Afghanistan in July 2009, was part of the Walking with the Wounded race to the pole expedition along with Prince Harry.
The rival teams faced such extreme weather conditions that organisers had to call off the competitive element. But the UK team and squads from the US and Commonwealth made it to their Antarctic goal on December 13.
The 34-year-old, originally from Muir of Ord, near Inverness, said: "It was a big disappointment when the race was called off but some of the guys were really struggling, some had frostbite, so I can see why they did it."
Hugging daughter, Lilly, he added: "I'm just happy to be home to this little one."
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