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The baby was born Aug. 10, a rep for Lee says. No other details were announced.
Lee's rep announced the pregnancy exclusively to PEOPLE, then the actor let it slip on the Today show that the couple were expecting a girl.
Lee, 38, also has a 4-year-old son, Pilot Inspektor, with his ex, actress Beth Riesgraf.
JOSH & FERGIE: ROCKED BY SCANDAL
Did he cheat with a stripper?
Married less than a year, the couple denies an Atlanta woman’s claims that she and Josh had a fling
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