He was named Eric, after Cowell's father, and weighed 6lbs 7oz.
The music mogul, 54, spoke of his joy at the birth on Twitter, saying: "Very happy to say Eric was born at 17.45pm. Healthy and handsome.
"Lauren in great shape. Thanks for all of your kind messages. Named after my dad."
The X Factor judge had jetted over to New York and was by his partner's side as she gave birth.