The couple - who tied the knot in Oxfordshire, South East England, last June - will welcome a baby into the world this winter, with journalist Celia being four months pregnant, according to the Mail on Sunday newspaper.
Chat show host Piers - who already has three sons from his 20-year marriage to Marion Shalloe, whom he divorced in 2008 - first met Celia on a photoshoot, claiming she was "way out" of his league.
He then proposed to the 34-year-old beauty while on a romantic trip to Paris by presenting her with a book by her most-loved writer John Updike, entitled 'Marry Me'.
READ MORE:Paris Hilton peddles her new show 'The World According to Paris' on Piers Morgan's show with sex tape and tearsPiers Morgan trying too hard to make an impression on CNN
The pair then tied the knot in a quiet ceremony, where he neglected to even invite fellow 'Britain's Got Talent' judge Simon Cowell to the nuptials.
He said: "I couldn't trust him to turn up on time."
Simon later retorted: "I hate to admit it but I'm absolutely thrilled for the two of them. Having met Celia, I have no idea how he managed to pull this one off."