Garner, 33, gave birth to the couple's first child at a Los Angeles hospital after labor was induced Wednesday night, according to Us Weekly magazine. A source told the magazine that Affleck, also 33, was by his wife's side in the delivery room, "the entire time."
Affleck and Garner first worked together in the 2001 film "Pearl Harbor," and co-starred in 2003's "Daredevil," in which he played the comic book hero and she was Electra, a part she reprised last year.
In June, the couple simultaneously announced their marriage and Garner's pregnancy. The baby, reportedly named "Violet," is the first child for both actors.
Affleck's previous relationship, with actress and singer Jennifer Lopez, turned him into a tabloid sensation.
The overexposure was said to have hampered his movie career. In 2004, he starred in such bombs as "Gigli," "Paycheck," Jersey Girl," and "Surviving Christmas." This is the first year since 1996 that Affleck has not appeared in a film.
Garner starred in the ABC television series "Alias," which will conclude its five-year run in May. Earlier this year, the plotline of the show was expanded to include the pregnancy of Sydney Bristow, her spy character.
Garner is expected to resume her film career soon. This spring, she began filming "Catch and Release," which is set to open next year.