"Stella and Alasdhair Willis are thrilled to announce the birth of their healthy and happy baby boy born in the early hours of February 25th in London," the couple said in a statement.
The couple's rep tells PEOPLE: "Both mother and father are thrilled with the news."
McCartney, 33, wed Willis, 34, a former magazine publisher, in August 2003. This is the couple's first child. McCartney's father is former Beatle Paul McCartney.
The timing of the birth was not ideal. Stella McCartney is set to show her latest collection in Paris on Thursday. It's not known yet whether she'll be able to attend her show, but the show will go on either way.
Stella's father, Paul, 62, and his second wife Heather Mills, 37, have a 16-month-old daughter, Beatrice. Stella's mother, Linda McCartney, died of breast cancer in 1998.
Stella and Alasdhair's 2003 wedding was held at Mount Stuart, a 300-acre estate on the Scottish Isle of Bute. The lavish ceremony was decorated with three truckloads worth of white English Beauty roses from Holland and a 10-minute fireworks display. Guests in attendance included Madonna, Liv Tyler, Kate Moss and bridesmaid Gwyneth Paltrow.