Ronald Asadorian/Splash News
01/10/2008 AT 04:05 PM EST
Fashion designer Stella McCartney, 36, has given birth to her third child, a son, Beckett Robert Lee, PEOPLE has confirmed.
Born Tuesday in London, Beckett joins brother Miller Alasdhair James, born in February 2005
, and Bailey Linda Olwyn, born in December 2006
Dad is McCartney's husband, Alasdhair Willis, the chairman of a furniture company, and grandpa is Paul McCartney. Stella's mother, Linda McCartney, died of breast cancer in 1998.
first reported Beckett's arrival.
Reporting by SIMON PERRY