The touching black-and-white shots show the millionaire music mogul cradling his tiny son, gently patting his head and looking down lovingly at him in his arms as his American girlfriend Lauren Silverman caresses their child's head with the back of her hand.
Touchingly, Cowell, 54, also writes: " Mum, Dad and Eric. Now two days old.
"I never knew how much love and pride I would feel .... now you can see how very handsome little Eric is."
Little Eric, who is named after Cowell's late father, was born in New York on Valentine's Day at 5.45pm.
He weighed in at a healthy 6lb 7oz.
His arrival forced the X Factor supremo to hurriedly ditch judging auditions for Britain's Got Talent to jet over in time for the birth.