John concluded his post with #NotJustanUncleAnymore and #Overjoyed hashtags, referencing to his character as Uncle Jesse on the sitcom.
Accompanied was a black and white photo of the actor with the newborn.
Billy is named after Stamos' late father, William Stamos, who was always supportive of John's acting aspirations gave his blessing when John wanted to drop out of college to be an actor.
"From now on, the best part of me will always be my wife and my son".
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The Full House alum has been vocal in the past about his lifelong desire to be a father.
This is the second marriage for John, who was married to Rebecca Romijn from 1998 to 2005.
"I'll be a fun dad".
He previously said: "It's just taken me a lot longer than I anticipated".
To which Caitlin cheekily responded: "Because you're old". I have a youthful thing. "So I called her parents to ask, and it was like, 'You better!'" "And I said, 'Why?'" Stamos told People.
"The look on John's face when I told him we were pregnant was priceless", added Caitlin. Every day I say, 'You're doing so great, you're doing so great'.