People reports that the actor announced on his Website that his daughter, Vida Alves McConaughey, was born yesterday (January 3).
The star wrote, "Camila’s recovering wonderfully and we are both truly honored to welcome this little lady into our family."
McConaughey, 40, also has a 17-month-old son named Levi with Camila Alves, 26.
The couple, who began dating in 2006, announced that they were expecting again last June. They decided not to learn the sex of the baby and to keep it a surprise, just as they did for their first child.
Last June, it was announced that McConaughey was planning to marry Alves before the birth of their second child. The actor once spoke of not believing in marriage, but his tune has changed since becoming a father.