The 28-year-old "Glee" alum and the actor, 32, became parents to Josey Hollis earlier this month, reported Us magazine.
The baby shares the same name as Clint Eastwood's character in the 1976 film "The Outlaw Josey Wales".
"They are so excited to be first-time parents. It was a very easy pregnancy and birth. Naya was born to be a mother and is doing really great so far," a source said.
The actress and her husband of one year originally announced her pregnancy back in April on Instagram.
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