Credit: David Schumacher

Hola, Leo!

Late last week, Penelope Cruz and husband Javier Bardem took a sun-lit stroll in Will Rogers Park in Pacific Palisades, Calif. with a very precious package: Their brand-new baby boy!

Only has the first exclusive photos of the Oscar-winning Spanish couple doting over their adorable (and drowsy!) son, reportedly named Leo Encinas.

Surrounded by family members, Cruz, 36, gave birth to little Leo in late January at Cedars-Sinai Hospital in Los Angeles.

Dating since 2007, she and her Vicky Cristina Barcelona costar Bardem, 42, secretly wed in July 2010 in a small ceremony at a pal's house in the Bahamas.

The resolutely private couple have kept mum about their new pride and joy -- but Bardem couldn't help but get emotional about his family while accepting a Goya Award in his native Spain Feb. 13.

"I dedicate [this award] to my wife and son for awakening my heart and smile every day," the actor gushed.

In a July interview with Hola's website, Cruz's lookalike sister, Monica Cruz, revealed the obvious about the stunning couple: "[They're] so obviously very much in love."

"He's a friend and the best actor in the world," Cruz has said of her man.