Us exclusively broke the news of the New York socialite's pregnancy back in July. She and Cowell were initially reluctant to talk about their baby joy in public, as Silverman was still married at the time -- to Cowell's friend, no less -- but he opened up a few weeks later, telling Us he was "happy and excited" to become a father.
Later, in an October interview with Parade magazine, he spoke more about what he was looking forward to as a dad-to-be. "I'm not brilliant with babies," the acerbic TV personality confessed. "I never know what to do. But [once he's older] I think I'll be a good dad in terms of advice. And then I'll get to do all the things I want to do, like go to Disneyland or Universal Studios, teach him how to drive -- I love all that."
His approach to parenting, he said in a different interview with Extra's Terri Seymour (his ex-girlfriend), would be something like his father's. "Be cool about it. You know, don't worry about things too much," he explained. "The way me and my brother were brought up, I mean, it was kind of relaxed. There were no self-help books or any of that crazy stuff."
"I want to teach him how to do my job as quickly as possible," joked Cowell, whose production company, Syco, launched "The X Factor" and "America's Got Talent," among other shows. "I want to pass the reins over. I really would like the idea of teaching him how to run the business."
Keep clicking to see more pics of the new parents!