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

"Welcome Billy Stamos (named after my father)," Stamos captioned a photo of his newborn son nestled on his chest

Have mercy — John Stamos is a dad.

The Fuller House star announced the news on Instagram, revealing he and wife Caitlin McHugh have welcomed a son. Born at 8:32 p.m., William Christopher Stamos arrived on Tuesday, April 10 in Los Angeles, PEOPLE confirmed via his birth certificate.

“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”

A rep for Stamos tells PEOPLE mom and baby are happy, healthy and home from the hospital, while Stamos’ on-screen niece Jodie Sweetin raves in a statement to PEOPLE that she and their costars are “over the moon” for the couple.

“I am so thrilled for John and Caitlin!” she says. “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!”

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On Monday, McHugh shared a hilarious Instagram video of the couple waving a rattle at their “baby” — which the viewer soon learns is actually Star Warsmost famous droid, R2D2.

“Are you sure that’s our baby?” Stamos asks his wife, who replies, “Of course I’m sure!”

“I thought he’d have better hair,” the actor says. “He does have your eye.”

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

In an emotional December Instagram post, Stamos remembered his late father as he wrote about becoming a dad. “I will certainly fall short of the father my pop was, but – I’m going to give it my all! #Balance #BillStamos#Hero,” Stamos captioned a throwback picture of the two.

The actor previously told PEOPLE, “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.”

“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.”

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RELATED VIDEO: John Stamos on Why He’s Finally Ready to Be a Dad at 54

Stamos and 31-year-old McHugh, who wed Feb. 3 after two and a half years together, announced their pregnancy to PEOPLE exclusively in December.

“I always wanted to be a dad. Clearly I had to do some work on myself first,” the actor said. “I have a youthful thing. People say, ‘Oh, you look young.’ You start believing you’re gonna live to be 150.”

He added, “And then you wake up and go, ‘No, man, this is it. This is not a rehearsal.’ … People would say, ‘You should have a child.’ I was like, ‘That ship has sailed.’ ”

But Stamos said he felt prepared for parenthood.

“I’ll be a fun dad. I’ve been practicing for a long time,” he told PEOPLE, joking, “I’ve done every schtick you can do with a baby on TV … all the bits and jokes and diaper gags. I’ll probably just do all that stuff.”

Jokes aside, McHugh has no doubt her husband will be confident in his new role. As she told PEOPLE, “The look on John’s face when I told him we were pregnant was priceless. It was the look of a man who has wanted a family of his own but wasn’t sure it was going to happen for him. Now it is!”

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