John Stamos & Caitlin McHugh's Baby Is Here & His Name Is A Tribute To Someone Important

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As of this week, John Stamos has officially entered fatherhood. On Sunday, Stamos and wife Caitlin McHugh welcomed a baby boy, making the Fuller House star a father for the very first time. And according to an Instagram post that he made announcing the news — and sharing the first photo of his baby boy — it sounds like their little one is now the namesake of someone very important in his life.

Stamos shared the post in the early hours of Monday morning, including an adorable black and white photo of his new baby laying on his chest and gripping his finger. Even though the baby's face isn't shown in the picture, it's obvious there's a lot of love there already. "From now on, the best part of me will always be my wife and my son. Welcome Billy Stamos (named after my father)," he wrote, adding the hashtags "#NotJustanUncleAnymore" and "#Overjoyed."

As Stamos said, Billy's name comes from his late grandfather, Bill Stamos, who John was very close to before his death in 2001. Considering their close relationship, it makes sense that Stamos would want to honor him in this way — and baby Billy gets to have a part of his grandfather with him, even though they never got to meet.

Although Stamos frequently talks about his father, lately, the posts he's been making about him often have top do with becoming a father himself. In all the photos he's posted so far, it's clear that Stamos truly loved and admired his dad, so it's a given that he'd decide to name his own son after him. In March, he shared this picture of his dad looking in at him as a newborn, adding, "Can't wait to look at my baby like this."

Last December, Stamos and McHugh (who tied the knot in February) announced their pregnancy, revealing to People that he was becoming a father for the first time at 54. He explained that, although he thought "that ship had sailed," they decided to have a child before they were married, although an engagement came quickly after McHugh found out she was pregnant.

And of course, shortly after the word was out, Stamos took to Instagram to share another throwback photo of him with his dad, admitting that he would "certainly fall short" of the father that Bill Stamos was, but that he'd try his best. It's obvious they had such a sweet relationship, and it's undoubtedly a tradition that Stamos will continue now that he has a son of his own.

“The look on John’s face when I told him we were pregnant was priceless,” McHugh told People in the interview announcing that they were expecting. “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!”

“I’ll be a fun dad," Stamos added. "I’ve been practicing for a long time. 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.”

Anyone who's seen Full House (and now, Fuller House) can definitely agree with that statement. Obviously, being a TV uncle is a lot different than being a father to a child of your own offscreen, but at least he's had years of experience working with kids.

Congratulations to Stamos and McHugh. It's going to be so much fun to follow their journey into parenthood — especially knowing the adorable Instagram photos that are likely on the way.