McConaughey and Alves have dated for about two years.
Alves, a model and handbag designer, gave birth to her and McConaughey's first child Monday night, the actor's representative Alan Nierob told People.
"They're so happy!" a friend told the magazine.
The report didn't mention the baby's name.
McConaughey has starred in the movies "A Time to Kill," "Sahara," "We Are Marshall" and "Fool's Gold."
Notable deaths of 2014 [PHOTOS]