The couple, who have been together for two years, became engaged on October 22 in Disneyland.
"I always wanted to be a dad. Clearly I had to do some work on myself first," the Full House alum told People in December.
"I have a youthful thing. People say, 'Oh, you look young.' You start believing you're gonna live to be 150.
"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.'"
The couple have not revealed the gender of their child.
Stamos stars in Netflix's 'Fuller House' and spent part of 2017 with The Beach Boys as a drummer. McHugh has had guest spots on 'The Vampire Diaries' and 'NCIS: Los Angeles.'
The actor was previously married for seven years to actress Rebecca Romijn, before their divorce in 2005.
John and Rebecca married in 1998, and their divorce was finalized in 2005.