Named for the singer's grandmother, Violet weighs 6 lbs., 15 oz., and measures 21 inches – or as her rocker dad describes her, "just perfect."
Father, mother and child are happy and healthy, says the rep.
Grohl, 37, wed Blum, 29, a former MTV producer, at their Los Angeles home on Aug. 2, 2003, before guests including Clive Davis and Grohl's former Nirvana bandmate Krist Novoselic.
It was the first marriage for Blum and the second for Grohl, who was divorced from photographer Jennifer Youngblood in 1997.
After the Foo Fighters failed to win a Grammy in February, Grohl pointed to his pregnant wife and said, "I don't need Grammys anymore, baby! I'm retiring. I'm going to write a children's book. Isn't that what you're supposed to do when you have kids? Or form a kid's band."
Grohl added that he'd been playing music to his unborn child: "Likes the Beatles. Doesn't really get down to the Beach Boys. Digs Mozart."