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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Tuesday afternoon's weather for the west of the region
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Two private citizens have already paid a "significant deposit" to take the week-long trip.