The music mogul from Sussex, aged 54, had jetted over to New York and was by his partner's side as she gave birth shortly before 11pm.
A spokesman for the X Factor judge said: "They are all OK. Simon was there for the birth. He landed at 6.15pm, British time, and he was at the hospital by about 7.15pm.
"He was there for the birth."
He said details about the baby, including how much he weighed, were not available yet.
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Amanda Houston has Wednesday's forecast for the west of the region.
Amanda has Wednesday's forecast for the east of the ITV Meridian region.
Amanda Houston has the lunchtime forecast for the west of the ITV Meridian Meridian region.