"[I thought] oh my God, this is exciting, and it's going to be a bit of a nightmare for the next few weeks," Cowell told Ellen DeGeneres in an interview scheduled to air Tuesday on Ellen.
"Because everyone knows, it was well documented, it was kind of uncomfortable. You know, the situation," Cowell said. "But these things happen and everything is kind of calm now and I'm happy. I'm actually happier than I've ever been."
News broke in July that Cowell was expecting his first child with the socialite—who was still legally married at the time to Andrew Silverman, a good friend of Cowell's.
It sparked a media frenzy.
"I can't blame the media because they've got a juicy story, but there was a lot of stuff said about her, that she trapped me and that she's a gold digger. Absolute nonsense," he continued. "She's a great girl, but it was awkward because of the circumstances."
While Cowell stayed mum on whether the couple is expecting a baby boy, he said their child will be raised in "New York, Los Angeles and London."
The media mogul recently gushed about fatherhood to the BBC, telling the network, "I'm proud to be a dad. It's something I haven't thought of before, and then, now I know I feel good about it. And she's [Silverman] a very special girl."