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."
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