In the book called "Total Recall," due out next week, Schwarzenegger says that it was on Jan. 4, 2011, when he and Shriver entered a therapist's office for a meeting initiated by her the day after his term as governor of California came to an end.

"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,'" the actor and former pol wrote in the book. "I told the therapist, 'It's true.'"

Schwarzenegger says he then started groveling, telling his wife that he had "screwed up" and that she was the "perfect wife," and that he was still "turned on" by her. It didn't work, and Shriver separated from him, and later filed for divorce.

In the book, Schwarzenegger says he had sex with housekeeper Mildred Baena in 1996 in the family guest house while Shriver and their kids were away on vacation and he was in town filming "Batman and Robin."

Schwarzenegger, 65, says that for years he tried to convince himself that Baena's husband was the father of their son, Joseph. But when the boy grew up and the resemblance to Schwarzenegger was so strong, he writes, "I realized there was little doubt that he was my son."

This hiding of the tryst and his secret speculation about his biological son all happened while Schwarzenegger watched as Shriver defended him from allegations of infidelity.

"I am my own woman," Shiver said in a 2003 appearance on "Oprah." "I have not been, quote, "bred," to look the other way."

Schwarzenegger says he kept the affair and the fact that he was Joseph's father a secret partly because he was embarrassed, and also because he didn't want to face up to his wife's family, the Kennedys.

"Instead of doing the right thing, I'd just put the truth in a mental compartment and locked it up where I didn't deal with it every day," he writes.

In the book, Schwarzenegger also notes a parting shot he says Shriver, 56, took after their marriage ended. During the funeral for her father, Sargent Shriver, his now ex-wife described the respect he had for her mom.

"The way he admired her and respected her, when I think about it today, it actually takes my breath away," she said.

Schwarzenegger, who was in the audience, says that comment might have been "partly directed at me."

Schwarzenegger says he still doesn't know why he cheated, but that it was probably a mixture of stupidity and arrogance, he writes.

The star also writes that he still hopes to reunite with Shriver.

"You can call this denial," he writes. "But it's the way my mind works."