The 54-year-old Stamos posted a photo his son's arrival to Instagram, saying, "From now on, the best part of me will always be my wife and my son. Welcome Billy Stamos."
He tagged the photo: "#NotJustanUncleAnymore #Overjoyed."
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Billy is named after John's father.
In December, the Full House and Fuller House star announced that he and fiancee Caitlin McHugh were expecting a child in an interview with People Magazine.
Stamos, who is a first-time father, said he was ready because he's had "years of practice."