6:00 AM PST -- Matthew posted on Facebook ... Camila gave birth to a baby boy, who they named Livingston.
Matthew McConaughey's wife just popped out baby #3 ... TMZ has learned.
Sources tell us ... Camila Alves gave birth earlier this morning at a hospital in Austin, TX. We're told Matthew was there, he was ecstatic for the new arrival (clearly) ... and even looked like he'd packed on a few pounds.
You'll recall ... the actor announced news of the pregnancy back in July, tweeting "Happy birthday America, more good news, Camila and I are expecting our 3rd child."
We haven't confirmed yet, but sources close to the situation tell us ... it's a baby girl!
FYI -- The duo met in 2006, but didn't get married until June 2012. They have two other children: Levi (4) and Vida (2).