Showbiz
Rex Features
The couple, who have been dating for two years, welcomed their first child in Los Angeles on Monday.
McConaughey said in a statement: "Levi was another name for the apostle Matthew in the Bible. They were, in fact, two names for the same person.
"Our son was born at 6:22 pm, and this particular time represents my favourite verse in the book of Matthew in the Bible: 'If thy eye be single, thy whole body will be full of light.'"
The actor explained that the middle name Alves was chosen to incorporate his girlfriend's surname.
He added: "We welcome Levi Alves McConaughey into this wonderful life and look forward to living in it with him. In the meantime and all times, just keep livin'."
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