The It Takes Two presenter - who already has a son, Jake, eight, and a five-year-old-daughter Matilda - was said to be 'overjoyed' with her new arrival.
Claudia, 39, and her TV producer husband Kris Thykier have named their new son Arthur.
The couple separated for a brief period in 2008, with Claudia being spotted out minus her wedding ring. She later said: 'Everyone has problems, but you have one life and you have to sort things out. It's what everyone does'.
Claudia announced her pregnancy on Twitter in March.
Congrats Claudia and Kris!