Silverman, 36, gave birth on Valentine's Day in Lenox Hill Hospital's executive suite in Manhattan at 5:45PM, the New York Daily Newsreported.
Cowell said his "very handsome" baby boy was named Eric after his father and was born weighing "six pounds, seven ounces."
Cowell also told the Daily News his girlfriend is "doing fine and healthy" and his son is "incredible," adding that "it feels great" to be a first-time father.
On Sunday, Cowell expressed on Twitter how his first weekend went as a new dad in addition to posting numerous photos of his family.
"The last three days have been incredible. Eric Lauren sqiddly and diddly all happy," he tweeted.
The suite Eric was born in reportedly costs up to $2,400 per night. When Silverman went into labor late last week, Cowell reportedly rushed out of a Britain's Got Talent taping in the U.K., boarded a private jet and headed to New York to be at his girlfriend's side.
News of the pregnancy first surfaced in July when Silverman was still married to now-estranged husband Andrew Silverman -- who used to be Cowell's close friend. The "adulterous affair," according to TMZ, ended the couple's marriage and led Andrew to file for divorce on July 15 -- citing adultery and naming Cowell a co-respondent.
Cowell hinted in September of last year he may propose to and marry Silverman since they're having a child together.
"Let's put it this way, I wouldn't expect her to be a single mother," Cowell told Ryan Seacrest several months ago during an appearance on his On-Air with Ryan Seacrest syndicated radio show.
Lauren and Andrew signed a divorce settlement in November. They have a seven-year-old son together.
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