The X Factor boss became a father for the first time in February when his girlfriend Lauren Silverman gave birth.
Cowell shared the pics with his followers on Twitter, showing the 11-week-old in a striped babygro, with one of the images depicting him in Silverman's arms, staring at her face.
He told his fans: "My little boy Eric is healthy and happy."
And in a caption to another of the images, in which Eric appears to be clambering on a sofa in a sunlit apartment, he wrote: "Very handsome like his dad."
Cowell said he was travelling back to the UK from his Los Angeles base, adding: "Hope you are enjoying Got Talent. Next week's show has a very special audition."
The next heat of the programme on Saturday also coincides with the final night of his X Factor musical I Can't Sing! which has proved to be a huge box office flop.
The London Palladium production, which had months of publicity ahead of its launch, is closing a little over six weeks after its official opening night.