The Hollywood couple, who already have daughters Violet Anne and Seraphina Rose together, are said to have welcomed a baby boy in Santa Monica earlier this week.
Affleck and Garner have not yet revealed their son's name, a source told People magazine.
When asked if Affleck was hoping for a boy last month, Garner said told Jay Leno on his chatshow: "At first, I think, I really thought so. And then he kind of said, 'Well, we have girls. We know how to do girls. My girls love me. I'm the big guy in the house.' So, now I'm not sure."
She also said that although it would be "weird" to have a son, it would also be "cool and different".
After announcing her pregnancy, Garner admitted that her daughters had been choosing potential baby names for their new sibling, saying: "At first they were definitely Disney. It was like, Donald Duck, Minnie Mouse Affleck. And then they've moved on. Then it was Peter Pan, Captain Hook, Smee."
During her pregnancy, Garner joked that she felt and looked like she was 17 and a half months pregnant.
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Watch Jennifer Garner on The Tonight Show with Jay Leno below: