In an autobiography to be published next month, Schwarzenegger says he "wanted" for years to believe that the boy, who was born in 1997, was not his.

But as he grew up the physical resemblance became so strong "I realised there was little doubt that he was my son".

Schwarzenegger and his wife, Maria Shriver, a niece of former US president John F Kennedy, separated last year after he confirmed he had fathered the boy, Joseph, on Mildred Baena, their Guatemala-born housekeeper.

A copy of his book Total Recall: My Unbelievably True Life Story, was obtained by the New York Daily News. According to the newspaper, it details Schwarzenegger's visit to a couples' counselling session on January 4.

He thought it was to help him and his wife, with whom he has four children, make the change from public to private life.

He wrote: "The minute we sat down, the therapist turned to me and said 'Maria wanted to come here today and to ask about a child - whether you fathered a child with your housekeeper, Mildred.'

"I told the therapist: 'It's true'."

The former Mr Universe is said to recount in the book that his illegitimate son was conceived in the guesthouse of his home while his wife was away. At the time he was making Batman and Robin.

He blamed his own arrogance in believing "you'll get way with ignoring the rules" for what happened. Shriver asked him about the parentage of the child several years ago but he denied it.

While Schwarzenegger was governor, the housekeeper's husband left her and he began financially supporting her and the child.

He reportedly reasoned this was politically acceptable because he had not campaigned on family values. The book is part of an effort to rehabilitate his image.