The music mogul tweeted a beautiful photograph of his son, who is called Eric Phillip and is just five days old, sleeping snuggled in a grey blanket. On one side of him is a grey knitted elephant and on the other is a beige teddy with a bow.
"Eric's new friends," wrote proud dad Simon alongside the picture early on Tuesday morning.
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It didn't take The X Factor judge long to show his adorable baby boy to the world. When Eric was just two days old Simon, 54, shared photographs of his new family on Twitter.
"I never knew how much love and pride I would feel," he wrote, after posting three adorable pictures of his son.
The X Factor judge, whose partner Lauren Silverman gave birth to their son on Valentine's Day, is seen tenderly cradling his son in two of the snaps.
Another image is a heartfelt family shot captioned, "Mum, Dad and Eric."
Simon wrote: "… now you can see how very handsome little Eric is."
Eric is named after Simon's late father Eric Selig Phillip Cowell, who died of a heart attack in 1999 at the age of 81.
Lauren was admitted to Lenox Hill Hospital in New York City on Friday after she went into labour that morning. Their son was born at 5.45pm weighing six pounds and seven ounces.
The couple were pictured leaving the hospital on Sunday. Simon, wearing a white t-shirt and jeans, aviator shades and a long coat, held on tightly to the car seat carrying his precious cargo as the pair left the NY hospital.
Lauren, 37, was dressed in black and looked radiant three days after giving birth, her hair falling in waves around her face.