updated 08/24/2011 AT 12:15 PM ET
•originally published 08/22/2011 AT 5:30 PM ET
Kimberly Stewart received a very special birthday present Sunday – her daughter.
The actress and model celebrated turning 32 by giving birth to a baby girl named Delilah in Los Angeles, PEOPLE confirms. The father is Academy Award-winning actor Benicio del Toro, 44.
Calling the arrival of his first grandchild one of the happiest days of his life, proud grandfather Rod Stewart tells PEOPLE, “My joy is indescribable.”