The couple already has two children, son Levi, 4, and daughter Vida, 2. They announced the news and the name of their newborn baby via the actor's account of social site whosay.
McConaughey wrote: "Our son, Livingston Alves McConaughey was born at 7:43 a.m. on 12.28.12. He greeted the world at 9lbs and 21 inches. Bless up and thank you for your well wishes. Happy New Year, and just keep living."
McConaughey and Alves dated for six years, before getting married in April this year.
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