The wonderful addition to the family comes soon after John and Caitlin tied the knot in February.
The actor announced his good news on Instagram on Sunday with a sweet photo of his newborn son, Billy, resting on his chest.
The caption reads "From now on, the best part of me will always be my wife and son. Welcome Billy Stamos (named after my father) #NotJustanUncleAnymore #Overjoyed", he wrote alongside the picture.
The 54-year-old, well known for playing Uncle Jesse on Full House, shared the exciting baby news on Instagram with this photo.More news: Samsung smartphone for students to avoid exam distractions
The Full House alum has been vocal in the past about his lifelong desire to be a father.
Stamos announced he was going to be a father back in December.
To which Caitlin cheekily responded: "Because you're old". "And I said, 'Why?'" Stamos told People.
"From now on, the best part of me will always be you". I know my parents are smiling down.
She described it as the look of a man who wanted to be a father his whole life but thought the moment had passed. Every day I say, 'You're doing so great, you're doing so great'.