updated 01/26/2010 AT 2:00 PM ET
•originally published 01/26/2011 AT 10:45 AM ET
Penélope Cruz and husband Javier Bardem have a new co-production.
Cruz, 36, delivered a son over the weekend at Cedar-Sinai Medical Center in Los Angeles, a source tells PEOPLE. Reps for the couple have yet to confirm the birth of the baby boy, whom a source says remains unnamed. The news was first reported in Spanish newspaper El Pais and Hola! magazine.
Sources tell PEOPLE that Cruz had a baby shower at her Beverly Hills home on Jan. 16. The actress had revealed she was pregnant last September, after being spotted with an obvious bump on the set of her upcoming film, Pirates of the Caribbean: On Stranger Tides.
Shortly after that, Bardem, 41, spoke about his excitement over becoming a father, saying of his wife’s pregnancy, “I am very happy.”