April 16, 2018 04:00 PM

Dave Coulier couldn’t be happier that his close friend and Fuller House costar John Stamos has finally become a father.

“He’s talked about it since I’ve known him, which is over 30 years,” the 58-year-old actor tells PEOPLE, hours after Stamos, 54, announced that he and his wife Caitlin McHugh had welcomed their first child, son Billy.

“Caitlin couldn’t be a better mom and a better partner for him. We are very excited to welcome her to the family,” Coulier adds.

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RELATED: It’s a Boy! John Stamos Welcomes Son Billy — and Names the Newborn After His Late Dad

Announcing the happy news on Sunday, Stamos went on to share the heartfelt story behind the newborn’s name.

“From now on, the best part of me will always be my wife and my son. Welcome Billy Stamos (named after my father),” the proud papa wrote alongside a sweet picture of his son nestled on his chest.

While the name may have come as a surprise to fans, Coulier says he knew the baby’s “name would be Billy” when Stamos and McHugh, 31, tied the knot in February.

“I was very close to John’s dad Bill, we were golf buddies. We shared a ton of laughs together while he was still alive,” Coulier tells PEOPLE. “I know John looked up to his father immensely. I think it’s only fitting that his son’s name is Billy.”

Dave Coulier
Paul Archuleta/FilmMagic

In an emotional Instagram post last year, Stamos remembered his late father as he wrote that he would “certainly fall short of the father my pop was.”

The actor previously told PEOPLE that “till the day he died,” his father “was bigger than life to me.”

“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 said.

RELATED: John Stamos Jokes He “Needed Years on Television” Before Becoming a Father

Coulier also adds that while it took “a long time” for Stamos to feel ready to become a parent, the actor’s journey towards fatherhood “was a natural progression.”

“For a long time he wasn’t ready and I think as life progressed it just became something that he really gravitated toward and it was a natural progression for him. I’m so happy for him. He’s going to be an incredible dad,” the actor tells PEOPLE.

But just because Coulier knows Stamos will make a great father doesn’t mean he thinks Stamos won’t have his work cut out for him.

“John had a lot of practice with the Full House kids but that was not on the job training. Now he’ll have to actually change diapers!” jokes Coulier, who has a son of his own, adding one very important piece of advice for the new dad: “Always wash your hands in between changing diapers and the next meal.”

John Stamos, Lori Loughlin and Dave Coulier
Kelly Lee Barrett/Getty

RELATED VIDEO: John Stamos Says He’s Going To “Be a Fun Dad”

Coulier isn’t the only one of Stamos’ Fuller House costars to send their congratulations to the new dad. In a statement shared with PEOPLE, Candace Cameron Bure sent her best regards to the happy couple saying, “Congratulations to John and Caitlin!”

“Billy is blessed to have you as Mom and Dad! Seeing John ‘parent’ over the last 30 years to all his nieces, nephews and TV babies, there’s no doubt how much Billy will be loved,” she added. “And they all lived happily ever after. Congratulations!”

Raved Jodie Sweetin in a statement to PEOPLE, “I am so thrilled for John and Caitlin! He’s been such an amazing part of my family for over 30 years, and to see him so happy and blessed with a beautiful little boy is wonderful. The entire FH family is over the moon and we can’t wait to meet little Billy!”

John Stamos and Caitlin McHugh

A rep for Stamos previously told PEOPLE that both mom and baby are happy, healthy and home from the hospital. And on Monday, McHugh shared a hilarious Instagram video of Stamos playfully questioning her about whether she was “sure” Billy was their child.

“I thought he’d have better hair,” the actor joked, before conceding that their “son” (who turns out to be Star Wars‘ R2D2) did have his mother’s “eye.”

The Disney super fan and new mom captioned the cute clip, “Our son Billy is clearly taking after my side of the family 😉💙.”

Asked whether a Fuller House celebration was in the works, Coulier tells PEOPLE it’s only a matter of time.

“We will all get together, we all get together all the time. we just haven’t been able to yet. Fuller House starts up soon so I’m sure we will throw a little party for him,” he explains.

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