The actress, 36, became a mummy for the first time on Thursday (29 May) her rep told People.
A statement says: "Both mum and baby are doing great."
The name of the baby boy has not yet been released.
Ginnifer and Josh, 32, both star in Once Upon A Time together, playing on-screen couple Snow White and Prince Charming.
After falling in love on set, they got married on April 11 in an intimate ceremony in Venice, California surrounded by close family and friends.
They announced her pregnancy last November, a month after they told fans they were engaged.
At the time, they said: "We are so thrilled... and can't wait to celebrate with our friends and family, including our second family at Once Upon A Time."
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