John shared a heartwarming photo of Billy lying on his chest on Instagram, writing in the caption: "From now on, the best part of me will always be my wife and my son. Welcome Billy Stamos (named after my father) #NotJustanUncleAnymore #Overjoyed."
The Fuller House star previously spoke of missing his parents during this time in his life.
"It kills me that my parents aren’t here to be part of this, but I know it probably wouldn’t be happening if they weren’t up there," he told PEOPLE. "You know how you put your father on a pedestal, and he’s a superhero, and then as you grow older, you go, ‘Ah, he’s just a man’? I never got to that point. Till the day he died, he was bigger than life to me."
It seems the actor has found a way to honour his father.
Congratulations to the happy couple!