"Elizabeth Hurley is delighted to announce the birth of her son, Damian Charles," a spokeswoman for the model-actress said in a statement.
"Both mother and baby are happy and healthy."
Steve Bing, who has questioned whether he is the father of the baby, has become involved in a bitter war of words with Hurley over the child.
The millionaire producer has also filed two libel suits against British newspapers.
The first, filed in London last January, responded to a Dec. 22 article in the Daily Mail that claimed that Bing had hired a private investigator to dig up dirt on Hurley with the aim of damaging the actress's reputation.
The second suit was against the Mirror after the tabloid called Bing a "sleazeball" and published his business telephone number with the suggestion that readers should pass on their opinions directly.
Bing, the grandson of New York real estate agent Leo Bing and the producer of such films as "Get Carter," reportedly began dating Hurley in the autumn of 2000.
Hurley, 36, who has appeared in movies including "Bedazzled" and "Austin Powers: International Man of Mystery," ended her 13-year relationship with actor Hugh Grant more than a year ago.
For several years she was the international face of Estee Lauder cosmetics.