Penélope Cruz gave birth to her baby daughter at Ruber International hospital on Monday.
"She's tremendously happy and very excited," said Javier Giner, the Spanish publicist of the 39-year-old actress.
The baby girl is the second child of the Academy Award-winning duo who first met in 1992 when they starred together in the classic comedy Jamon, Jamon.
The couple chose not to provide any more details about the new member of their family, as was also the case when Leonardo was born.
Cruz gave birth to a girl "just a few hours" after Kate Middleton welcomed her little boy in St Mary's Hospital in London on Monday, according to the online edition of Spanish celebrity magazine Hola!.
The low-key experience of Cruz and Bardem was in stark contrast to that of the UK's Duke and Duchess of Cambridge.
Crowds gathered in London on Tuesday with people hoping to catch a glimpse of the one-day-old boy who could one day be the King of England.
Giles Paxman, British Ambassador to Spain, wrote on Tuesday to the Duke and Duchess of Cambridge offering congratulations on the Royal birth, on behalf of the British nationals living in Spain.
"The Royal birth is happy and important news for the future of our country and I am delighted to send congratulations to Their Royal Highnesses on behalf of the many hundreds of thousands of British people who live in Spain. I’m sure it is a moment for expatriates to celebrate, just as it is for Britons back home.
"On behalf of the many British subjects living in Spain, I have the honour and pleasure to send our warmest congratulations to Their Royal Highnesses the Duke and Duchess of Cambridge on the birth of their first child."