"Penélope and Javier welcomed their first son into their family last week," Bardem's rep said in a statement. "Both parents and baby are doing great."
This is the first child for the Academy Award-winning couple, who quietly married in July. The two worked together on 2008's Vicky Cristina Barcelona, for which Cruz won an Oscar for best supporting actress. Bardem, 41, won the best supporting actor Oscar for 2007's No Country for Old Men. He received his third Academy Award nomination Tuesday — his first for lead actor — for his performance in Biutiful.
Cruz, 36, will next appear in Pirates of the Caribbean: On Stranger Tides, out this summer.