Affleck's publicist, Ken Sunshine, and Garner's spokeswoman, Nicole King, said the child was born at 6:26 p.m. ET Thursday, after several news outlets erroneously reported Garner had already given birth nearly five hours earlier.
"Mother, father and baby are doing great," the reps said in a statement. No further details were released.
Word about Garner's pregnancy first began spreading in May, nine months into her relationship with Affleck, 33. (The pair, who first met on the set of the 2003 movie Daredevil, began dating after Garner, also 33, split from her husband, actor Scott Foley, after 2 1/2 years of marriage.) Reps confirmed the pregnancy after the couple married June 29 in a small, low-key ceremony on the Turks and Caicos Islands.
Garner's pregnancy was written into this season's Alias storyline. And then, on Sept. 27's Tonight Show, Garner let slip to host Jay Leno that the baby was a "she."
"You can just start to feel really pregnant, like you are the hugest person on the face of the planet," said the actress. "I felt bigger and bigger, like she ... ." Garner then quickly covered her mouth with her hands, and the crowd cheered.
Up until that moment, Garner remained evasive about the baby. At the Sept. 18 Emmys, the nominated star admitted on the red carpet that she knew the gender of her child, but said she was keeping it secret.
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As for their new roles as Mom and Dad, Affleck's friend, director Don Roos, said they'll be great parents. "Ben's got the right woman and he's excited about this new chapter in his life. He's really excited about becoming a father and Jen seems ecstatic," he told PEOPLE in July.
Roos added: "I can't wait to see Ben change a diaper. He's so huge, and the thought of him standing over a 7-lb. baby … He'll be a great father. He's very patient. He's close to his mother, brother, father and family. What else do you need?"