Beau, which in French means “beautiful,” was born on Friday at 11:12 a.m. and weighed a healthy 7 lbs., 15oz.
Speaking outside London’s Portland Hospital, Jones said: “He is absolutely brilliant, and both baby and Emma are doing fine. In fact Emma is tucking into some flapjacks and Coca-Cola as we speak.”
The new father added, “We are both absolutely delighted and can’t wait to take Beau home.”
Jones, 27, is a former member of the British boy band Damage. He and Spice Girl Bunton, 31, have been together for eight years and moved into a five-bedroom home in her native north London in 2005.
Motherhood for the youngest of the reunion-bound five-piece has been difficult to achieve.
In 2000, Bunton had to have pre-cancerous cells removed from her cervix. Last year, she revealed she’d been diagnosed with endometriosis, a painful condition in which the lining of the uterus begins growing in other areas of the body, making it difficult to conceive.
Less than two months ago, Emma told PEOPLE: “I’m getting a little feisty now that I am pregnant.”