The tot weighed 7lb and the overjoyed couple have named their new arrival Milo Thomas Bugliari.
The 'Charmed' star's representative said: "Alyssa and her husband David proudly announce the birth of their son, Milo Thomas Bugliari. Milo Thomas was born on August 31 at 9.27am weighing 7 pounds and was 19 inches long."
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Alyssa, 38, took to her twitter account to share her joyous news and also thanked her followers for their congratulatory messages.
She wrote: "Thank you for all the well wishes for my son Milo. My heart has tripled in size. I love him more than all the leaves on all the trees."
Alyssa - who married David in August 2009 - knew she was having a son throughout the later stages of her pregnancy but was refusing to pick a name for her baby until she met him.
She previously said: "We have three names. You hear so many stories about people who picked a name out and then the baby didn't look like the name. So we're narrowing it down until we see the child. However, we will go with a slightly Italian name, so that it goes with Bugliari."