A rep for the couple confirmed the news to Access Hollywood on Thursday.
Alec first revealed that the couple were expecting in early February, Tweeting, "My wife is pregnant. To celebrate the announcement, she is teaching yoga."
The 54-year-old actor and the 28-year-old yoga instructor wed in June 2012.
The actor is already a dad to daughter Ireland, 17, from his previous marriage to Kim Basinger.
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