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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Wednesday's weather for the west of the region
Wednesday's weather for the east of the region
The Ashford International to Canterbury West rail line should reopen on Thursday. It has been closed since a train derailed on Sunday.