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Mattias Ferrell was born just after 2 a.m. on Dec. 30, Matt Labov tells the Associated Press.
Ferrell and Paulson, 37, an art auctioneer, already have one son, Magnus, 2.
In November, while on The Late Show with David Letterman to promote his movie Stranger Than Fiction, Farrell revealed that the baby would be a boy.
When asked if he knew the baby's gender, Ferrell, 39, responded: "You know, I don't know if I do," he said. "I've gotta check my BlackBerry."
He continued, "Well, we do know, but I forget if we're telling people. I told the Today show we weren't telling them. But it's a boy.
Asked by Letterman how Magnus was handling the idea of a little brother, Ferrell said, "He doesn't like it. He's in denial about it. ... I'm like, 'You better live it up now, cause No. 2 is coming and it's not going to be fun for you.'"
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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