asilverstonepart2042011_01_X17230WM.jpgUPDATE - Alicia's rep confirms what X17 reported first -- the baby has arrived! Silverstone gave birth to son Bear Blu Jarecki, 7 lbs., 15 oz., on Thursday.

Alicia Silverstone had the best Mother's Day weekend ever ... thanks to the birth of her new baby!

X17online can report exclusively that Silverstone had a water birth at an LA-area birthing center at the end of last week. We've learned the new mommy is already at home with her little bundle!

Throughout her entire pregnancy, the 34-year-old actress has been promoting her new diet book The Kind Diet ... which follows vegan principle.

Silverstone and hubby Christopher Jarecki, 40, confirmed they were expecting their first baby together back in January.

Wow ... time has flown by!