X Factor supremo Simon jointly held Eric, who was strapped into a car seat, along with a midwife as his little family headed for home.
In the early hours of today (17 February), Simon took to Twitter to tell his fans that the past few days have been "incredible" for him.
The British star also shared a snap of his pet dogs - Sqiddly and Diddly - curled up together, saying that all the loves of his lives were "happy".
Simon told his followers: "The last three days have been incredible. Eric Lauren Sqiddly and Diddly all happy."
The last three days have been incredible. Eric Lauren sqiddly and diddly all happy.— Simon Cowell (@SimonCowell) February 17, 2014
On Friday, Simon missed the London Britain's Got Talent auditions and flew to New York after Lauren went into labour.
Hours later, Simon declared that he was now a dad as Lauren had given birth to Eric - who is named after his late grandfather (Simon's dad).
Last night, Simon shared the first pictures of newborn Eric with the world by posting them on Twitter and Facebook.
He admitted: "I never knew how much love and pride I would feel."
Baby Eric weighed 6lbs 7oz when he arrived at 10.45pm UK time (5.45pm in New York) at Lenox Hill Hospital, NYC, two weeks earlier than Lauren's expected due date of February 28.
More celebrities who have welcomed babies in 2014:
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