The Britain's Got Talent judge, 54, left the UK on a private plane on Friday morning to be by Lauren's side as she delivers his first child.
Friends of the 37-year-old Lauren, who was not due to give birth for two weeks, have said she is not in full labour yet, but is showing "early signs".
Lauren wanted to give birth to her baby at home in Manhattan, to be near her mother and her eldest child Adam, from her previous marriage. She was due to give birth on 28 February in one of the city's most exclusive hospitals.
Speaking earlier this week, Simon said, "I am keeping my phone on during auditions 100 per cent. If it happens I have to go and dash on a plane.
"I probably will be nervous when it all happens. I am going to watch (film) Father of the Bride tonight to get used to that. I have got a feeling that my child is going to be really naughty."
The music mogul is currently overseeing Britain's Got Talent auditions in London's Hammersmith with co-judges Amanda Holden, David Walliams and Alesha Dixon.
He previously revealed that Lauren has given him the green light to carry on with his hectic work load.
"Lauren knows what my work schedule is like and everything else, so she's cool with that," said Simon. "We made the decision to come back to the UK and she wants to live here for a while."