Story Elias, was born on July 23 in Los Angeles weighing in at 7 lbs. 2 oz.
"He is already a fan of "classical music, a clean diaper, mom's boobs and long naps." adding that "Story wants to give big props to his mom for all the hard work."
Despite her pregnancy, Elfman made time recently to star in a short video on the humor Web site funnyordie.com – in which the pregnant actress schooled several players in a pickup basketball game.
This is the first child for the actress, 35, who played Dharma Finklestein Montgomery on the 1997-2002 ABC comedy and went on to star in the CBS sitcom Courting Alex, and Bodhi, 38, also an actor. The pair have been married since 1995.