John Stamos Said He’ll Be a ‘Fun Dad’ Months Before Welcoming Son Billy

Uncle Jesse is officially a dad and has a Full House of his own.

John Stamos announced on Instagram Monday that he and wife Caitlin McHugh welcomed a son named Billy. “From now on, the best part of me will always be my wife and my son. Welcome Billy Stamos (named after my father),” Stamos, 54, captioned a photo of the newborn nestled on his chest. “#NotJustanUncleAnymore #Overjoyed”

Before the birth of his baby boy, Stamos shared the pregnancy news exclusively to PEOPLE‘s Editor-in-Chief Jess Cagle in a December 2017 episode of The Jess Cagle Interview, discussing all things impending fatherhood and why he’s finally ready to be a parent.

“I’ll be a fun dad. I’ve been practicing for a long time. I’ve done every shtick you can do with a baby on TV … all the bits and jokes and diaper gags. I’ll probably just do all that,” said the actor, whose had father figure roles in TV series such as Netflix’s Fuller House and Fox’s now-canceled Grandfathered.

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Stamos also admitted that he “always wanted to be a dad” but wasn’t sure it was in the cards. “People would say, ‘You should have a child,’ ” he said. “I was like, ‘That ship has sailed.’ ”

Adding, “Clearly, I had to do some work on myself first. I have a youthful thing. People say, ‘Oh, you look young.’ You start believing you’re gonna live to be 150. And then you wake up and go, ‘No, man, this is it. This is not a rehearsal.’ ”

RELATED VIDEO: John Stamos Shares Baby News: ‘I’ll Be a Fun Dad’

Though playing several paternal roles in acting gigs prepared him for what fatherhood could be like, Stamos revealed that he had no better role model than his own father.

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“I had the best father in the world. 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 said of his father who passed away in 1989. (His mother, Loretta, died in 2014.)

“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,” he shared.

Also in January, Stamos opened up about his journey to fatherhood on The PEOPLE, Entertainment Weekly & TNT Official SAG Awards Red Carpet Live Show at the 2018 Screen Actors Guild Awards.

“I felt I needed years on television to do it, but apparently there’s no preparation,” he said. “It’s a wonderful time in life. I’m as grateful as I’ve ever been.”