Schwarzenegger admitted he had multiple affairs during his doomed 25-year marriage to Maria Shriver.
In a TV interview aired before his memoirs were published on Monday, the former bodybuilder and Hollywood star told how Shriver confronted him about the child the day after he left office as California governor in January 2011.
He also admitted he had a habit of living "in denial" and keeping secrets, including not telling Shriver that he was going to run for governor until days before he announced it and trying to conceal having heart surgery from her.
"That's the way I handle things. And it always has worked … it's not the best thing for people around me … [but] some information I just keep to myself," he told the CBS show 60 Minutes.
"So I became an expert in living in denial," he said.
Shriver filed for divorce in July last year citing "irreconcilable differences" with her husband, whom she met in 1977 and married in 1986, following him into the California governor's mansion in 2003.
Schwarzenegger had admitted in May 2011 that he had fathered a child, called Joseph and born in 1997, with the family's long-time housekeeper, Mildred Baena, and announced the couple's separation.
In the 60 Minutes interview, he said he realised when Joseph was about seven or eight that the boy resembled him physically, and while not discussing it openly, began giving his mother financial support for them.
The housekeeper remained in their employment and Joseph even played with the couple's children. But Shriver's suspicions grew and she finally confronted him the day after he left office when they saw a marriage counsellor.
Shriver asked him point blank: "Hey, I think that Joseph is your kid," to which he replied: "You're absolutely correct." She filed for divorced a few weeks later.
Baena was not the first time he had been unfaithful to Shriver, he acknowledged – in the book he writes about a "hot affair" with actress Brigitte Nielsen while filming the 1985 film Red Sonja.
Pressed in the CBS interview about other infidelities, he admitted: "I had others. But that's something between Maria and me," adding that Shriver knew about his behaviour.
"I'm not perfect," he said. – AFP