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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A damp and cold night ahead. Valentine's Day will start cloudy but become brighter in the afternoon. Risk of showers along the Kent coast.
Cold and damp tonight with outbreaks of rain. A cold and dull start to Valentine's Day but becoming drier and brighter by the afternoon.
Rain turning more patchy this afternoon but more persistent along the coast. Feeling cold in the brisk north-easterly wind.