Affleck's publicist Ken Sunshine and Garner's representative NICOLE KING confirmed press reports the ALIAS beauty had given birth to a baby girl at 6.26pm (EST) on Thursday.
The joint statement reads, "Mother, father and baby are doing great."
The DAREDEVIL co-stars representatives did not provide the baby's weight or place of birth.
Garner, 33, and Affleck, 33, started dating in July 2004, months after the actor ended his high-profile engagement to Jennifer Lopez (JAN04) and the actress divorced her first husband Scott Foley (MAR04).
They married on the Caribbean resort of Turks and Caicos on 29 June (05).