McConaughey's girlfriend, model and handbag designer, Camila Alves, gave birth to the child at 6:22 p.m. Monday.
"We welcome 'Levi Alves McConaughey' into this wonderful life and look forward to livin' it with him," Usmagazine.com said the actor wrote on his Web site, explaining that Levi is another name for the apostle Matthew in the Bible.
"They were, in fact, two names for the same person," he noted, adding that the time of his son's birth also has special meaning to him.
"This particular 'time' represents my favorite verse in the book of Matthew in the Bible, 'If thy eye be single, thy whole body will be full of light.'"
McConaughey said he and his girlfriend chose her last name as the child's middle name because "we wanted to incorporate her family name."
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