Moore also writes that in 2010 she saw media reports claiming Kutcher, 41, met 21-year-old Brittney Jones while bowling with Moore's daughter Rumer Willis, her daughter with Bruce Willis.
Moore claims Kutcher cheated on her with Jones in his marital home while she was out of town filming a movie.
Jones revealed to Star magazine: "I did all the suggesting in the texts, it was like he was paranoid and didn't want to text anything that would get him in trouble.
"I asked him if he wanted to meet, that's how we made the plans."
Brittney later claimed that Ashton was a "great lover."
When Moore confronted Kutcher, he brought up their threesomes as a defence.
Moore wrote: "Because we had brought a third party into our relationship, Ashton said, that blurred the lines and, to some extent, justified what he'd done."
Moore also accused the That '70s Show actor, to whom she was married from 2005 to 2013, of cheating on her again before their separation in 2011 while he was at his former co-star Danny Masterson's bachelor party.
Kutcher, who is now married to actor Mila Kunis, reportedly slept with 22-year-old Sara Leal, who gave her story about their affair to Us Weekly.
According to Radar, Moore learned about the alleged cheating from a Google alert.
"I felt sick to my stomach," she writes. "I knew she wasn't lying."
Earlier this month, the New York Times released quotes from the forthcoming book in which Moore, 56, detailed suffering a miscarriage six months into her pregnancy in the early 2000s. Moore "started drinking again and blamed herself for the loss", though she and Kutcher tried to conceive again through IVF.
Inside Out is set to be released on September 24.
