The couple - who tied the knot in June last year - are thought to have named their new daughter Elise although no further details of the birth are yet known, according to MailOnline.
While this is a first child for Celia, the 46-year-old chat show host has three sons from his 20-year marriage to Marion Shalloe, whom he divorced in 2008.
The pair first met on a magazine photo shoot and while Piers initially claimed the journalist was "way out" of his league, he later proposed to the 34-year-old beauty on a romantic trip to Paris by presenting her with a book by her most-loved writer John Updike, entitled `Marry Me`.
Piers and Celia then tied the knot in a quiet ceremony in Oxfordshire, 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."