The couple, who are already parents to two daughters, welcomed a baby boy in Santa Monica earlier this week.
Affleck has since confirmed on his official Facebook page: "We are happy to announce on February 27, Jennifer gave birth to a healthy baby boy, Samuel Garner Affleck."
Garner is believed to have been used as a middle name, rather than a double-barrelled surname.
The Valentine's Day actress gave birth to her first daughter with Affleck, Violet Anne, in 2005. They also have 3-year-old Seraphina Rose.
Garner revealed in January that the girls had suggested the new baby be named after a Disney character.
"It was like, Donald Duck, Minnie Mouse Affleck. And then they've moved on," she recalled. "Then it was Peter Pan, Captain Hook, Smee."
> Jennifer Garner: 'It would be weird to have a boy'