The actor couple welcomed the baby girl on July 22 in madrid as Luna Encinas Cruz, according to Spanish magazine, Vanitatis.
The magazine reports that Bardem, 44, visited Madrid's registrar office on July 30, where he registered their new child.
Luna means moon and the name takes on both her father and mother's paternal last names.
Cruz, 39 and the Spanish-born actor, who wed in July 2010, are already parents to 2-year-old son Leonardo.