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It's a Boy for Alicia Silverstone

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Alicia Silverstone is a mom!

The actress and author, 34, welcomed her first child with husband Christopher Jarecki on Thursday, May 5, her rep tells PEOPLE exclusively.

Son Bear Blu Jarecki arrived at 7:50 a.m. and weighed in at 7 lbs., 15 oz.

“We are all three in love!” the actress blogged soon after the announcement. “I’m so grateful to this community for all the love, support, good wishes and happy vibes you’ve sent me during my pregnancy … it has been wonderful. Thank you all!”

PHOTOS: Who’s Due Next?

She and Jarecki, 40, wed in June 2005 in Lake Tahoe after eight years together.

The author of vegan cookbook The Kind Diet, Silverstone will next be seen in the films Vamps and Butter.

Reporting by JULIE JORDAN