"We are all three in love," Silverstone wrote of the newborn, who weighed in at 7 lb., 15 oz. "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."
The Clueless actress, 34, did not say what the inspiration was for the name.
Silverstone and, musician Christopher Jarecki wed in June 2005 after eight years of dating.
What do you think of the name "Bear Blu"?