Billy is named after Stamos' late father, William Stamos, who was always supportive of John's acting aspirations gave his blessing when John wanted to drop out of college to be an actor.
The happy couple announced in a gushing Instagram post, which simultaneously confirmed that the baby has been named after Stamos's father. His publicist said that "Billy and mom are both home and healthy".
Jesse's no longer just an uncle!
The 54-year-old, well known for playing Uncle Jesse on Full House, shared the exciting baby news on Instagram with this photo.
A scene from "Full House", Oct. 19, 1993.
This is John's second marriage - he was previously Wednesday to actress Rebecca Romijn from 1998 to 2005.
The Fuller House star also admitted that he'd always seen his father as a hero, and the shine hadn't dulled in later life.
Stamos announced he was going to be a father back in December.
Stamos married McHugh, 31, on February 3, after dating for two and a half years. Then I said, I better have a ring on her finger because it's the right thing to do, and I wanted to marry her anyway.
"The look on John's face when I told him we were pregnant was priceless", smiled Caitlin. News. "I will say this".