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."
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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.
His baby son's middle name is also said to be a tribute to Topshop magnate Sir Phillip Green, who has been a huge support to the couple when Lauren was divorcing her husband Andrew Silverman.
"Simon wanted to pay proper tribute to the influence of his late father in his life," a source told The Mirror.
"But there's no doubt he also wanted to pay some kind of tribute to another Philip who has been a major influence in his life, Sir Philip Green," added the source. "It's tremendous he's been able to pay respect to two different role models with his baby."
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.
Lauren and her ex-husband Andrew have a son, Adam, eight, who was not present at the birth. "It's President's Day weekend and he had a pre-planned vacation with his father," a source revealed on Friday.