"We are overjoyed to announce the birth of our daughter. She is absolutely perfect," the 29-year-old yoga instructor wrote.
Alec Baldwin, 55, recently told People magazine he's looking forward to being a stay-at-home dad to the new baby.
"My dream is to be home with the baby, standing in the doorway, saying goodbye to Mommy," he said. " 'Mommy is going to work now. Bye Mommy ... don't work too hard!' "
Hilaria Baldwin said she doubted the "30 Rock" star's determination.
"At this point, before the baby is born, he thinks he's going to be Mr. Mom," she said. "We'll see if at 3 o'clock in the morning when the baby is screaming and we need to change the diaper if he's going to be Mr. Mom at that point."
Alec Baldwin already has one child, daughter Ireland, 17.