According to Spanish newspaper El Pais, the infant was born at Cedars Sinai Hospital in L.A.
Cruz, 36, first debuted her baby bump while shooting Pirates of the Caribbean: On Stranger Tides in Puerto Rico last September — just two months after she secretly tied the knot with Bardem, her Vicky Cristina Barcelona costar.
“He’s a friend and the best actor in the world,” Cruz has said of Bardem, 41.
The newborn’s name and gender have yet to be announced.