Two days later the music mogul shared three adorable black-and-white images of the tot and his proud parents.
"I never knew how much love and pride I would feel," wrote Simon, after posting three adorable pictures of his son. "Now you can see how very handsome little Eric is."
On 14 February Simon let his Twitter followers know the little boy had arrived safe and sound, writing: "Very happy to say Eric was born at 17.45pm. Healthy and handsome."
He later explained his choice of moniker: "Named after my dad," referring to his late father Eric Selig Phillip Cowell, who died of a heart attack in 1999 at the age of 81.
The latest update was posted shortly after Simon left hospital with his new little family: "The last three days have been incredible. Eric, Lauren (dogs) sqiddly and diddly all happy."
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.