It's a Boy for Jack Black, Wife

06/13/2006 at 07:50 AM EDT

It's a Boy for Jack Black, Wife
Jack Black and Tanya Haden
Kevin Winter/Getty
Jack Black and musician wife Tanya Haden, who eloped in March, are the new parents of a baby boy, born Saturday at Cedars-Sinai Medical Center in Los Angeles, Black's rep, Matt Labov, tells PEOPLE.

Black himself announced the arrival during Monday's Hollywood premiere of his new comedy Nacho Libre, telling TV's Access Hollywood, "Secretly, between you and me, it's already happened. I've got the babe back at home safe and sound, and I'm actually very anxious to get back to my lovin's (loved ones)."

Indeed, Black left the premiere shortly after the lights went down and the screening began.

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Black announced his wife's pregnancy last month while promoting Nacho Libre, in which he plays a wrestler who raises money for an orphanage.

"I think I will be good when it comes to playtime," he told reporters, according to USA Today. "I don't know how good I'll do with the discipline."

Black, 36, and Haden, 34, first met as students at Crossroads, a private high school in Santa Monica, Calif., and started dating in April 2005. They exchanged vows in a private ceremony in Big Sur, Calif.

It's a Boy for Jack Black, Wife| Birth, Jack Black

Black and Haden on June 2

Cousart-Rios / JFX

"They love each other very much. We're thrilled," the bride's father, jazz bassist Charlie Haden, told PEOPLE after the wedding.

In September, Black is set to begin filming Be Kind, Rewind, costarring Kirsten Dunst.

"Wherever the job goes, the baby is just going to come with me," he said last month. "It will work out." Besides, he joked, "I don't really get involved until he's, like, 10."

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