Update

Benicio del Toro, Kimberly Stewart Welcome Daughter

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.”

On Saturday, the singer had hosted a large group at Dan Tana’s to celebrate his daughter’s birthday, a source tells PEOPLE.

The following day, the clan – including dad Rod, mom Alana, stepmother Penny, brother Sean and half-siblings Ashley, Ruby, Renée, Liam and Alastair – visited with the family’s newest member.

“We had everyone at the hospital to help Kimberly, Stewart tells USA Today. “I won’t say we always agree, but we get along.”

The pregnancy was announced in April.

“Kimberly is pregnant. Benicio is the father and is very supportive,” del Toro’s rep confirmed to PEOPLE at the time. “Although they are not a couple, they are looking forward to the arrival of the baby.”

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