The 54-year-old has boarded a plane to the US to witness the birth of his son, and will miss Britain's Got Talent auditions in London today (February 14). Representatives for BGT confirmed to DS that Cowell will be missing auditions, adding that official comment on the baby reports will be delivered via his UK spokesperson.
Cowell told Digital Spy earlier this week that the baby will be born in New York.
Silverman, who divorced her real estate tycoon husband Andrew - a friend of Cowell's - last summer, is believed to have gone into labour two weeks early.
Meanwhile, the music mogul's confidante Sinitta appeared to allude to his baby news in a tweet earlier today.
If you think today is special... You are Right! Probably one of the most memorable days of 2014 already! Happy Valentines Day Baby! Xxx— Sinitta 19 (@sinittaofficial) February 14, 2014
Cowell first confirmed fatherhood rumours back at the One Direction This Is Us premiere in August.
Speaking to DS at BGT auditions on Tuesday (February 11), Cowell insisted that he is "good with kids" and the baby will "be well looked after".
The star admitted that he has already changed "a little bit" since discovering the news and said that he wants his son to take over the business.