The hut, made by Oxfordshire-based Red Sky Shepherd's Hut, now sits in the Camerons' garden.
Cameron told the company's owner he will use the hut as a writing room, according to a blog posted on the company's website.
Read more: Revealed: David Cameron's new jobs
However, the ex-PM will have to fight for the new space, with his son winning the battle to be the first to spend the night in the hut. Cameron said: "I wasn’t going to take him on.”
Cameron said: "There’s been a bit of a fight already - my children want to use it as a Wendy house. I want to use it as a book writing room and my son wants it as an alternative bedroom. So, quite a lot of competition."
The mobile huts have grown in popularity outside of their original shepherd community as they do not require planning permission, despite being fitted with heating and electricity.
The hut will more than pay for itself if Cameron does manage to use it for his intended purpose: his memoirs are expected to fetch £1.5m.
Cameron resigned as MP for his Oxfordshire seat of Witney in September, saying he did not want to prove a distraction for his successor as Prime Minister, Theresa May.
Since then he has occupied himself by becoming President of the Alzheimer’s Research UK, chairman of the National Citizens Service, as well as the obligatory tour of the lucrative public speaking circuit.