"The last three days have been incredible," wrote Simon, shortly after leaving hospital with his partner and son. "Eric, lauren (dogs) sqiddly and diddly all happy."
CLICK ON PHOTOS FOR GALLERY
Eager to show off his newborn baby, Simon has already shared the first photos of Eric.
"I never knew how much love and pride I would feel," he wrote after posting three pictures on Twitter. In two, the 54-year-old can be seen tenderly cradling his son, while the third is a touching family snapshot captioned, "Mum, Dad and Eric."
"…now you can see how very handsome little Eric is," Simon wrote.
Eric Phillip has been named after the X Factor star's late father, Eric Selig Phillip Cowell, who passed away in 1999 at the age of 81.
Lauren was admitted to Lenox Hill Hospital in New York on Friday after she went into an early labour. Simon jetted out of the UK to be by her side as she delivered their baby boy, who weighed 6lb 7oz and was born at 5.45pm.