The couple welcomed their third child together on Friday.
Matthew confirmed the news on his Whosay blog on Saturday night amid a flurry of reports about the birth.
"Camila gave birth to our third child yesterday morning,” he wrote before sharing the news of the baby boy’s name.
“Our son, Livingston Alves McConaughey, was born at 7:43 a.m. on 12.28.12. He greeted the world at 9 lbs., and 21 inches. Bless up and thank you for your well wishes,” the actor continued.
She opened up about having a difficult pregnancy back in August.
The model said she didn’t have much of an appetite.
“Thank God I’m not throwing up a lot, but food isn’t really appealing right now,” she said.
Matthew, 43, and Camila, 30, met at Los Angeles venue Hyde in 2006.
They were engaged on Christmas Day 2011 and married in Austin last summer.
They also share a four-year-old son, Levi, and a two-year-old daughter, Vida.