The 35-year-old television personality - who already has daughter North, two - gave birth to her second child on Sunday, nearly three weeks ahead of her due date of Christmas Day.
It has not been an easy pregnancy for Kim, who recently revealed she had to undergo an External Cephalic Version procedure to have her baby moved from the breech position.
She wrote: "This weekend I checked into the hospital and underwent a procedure called an ECV (External Cephalic Version, or a Version), which is done to manually turn the baby from a breech position to a head-down position.
"They gave me an IV with medication to relax my uterus, and then three doctors attempted to work together to turn the baby.
"There was a risk that my water might break or the baby's heart rate could drop - in which case, an emergency C-section would then take place. I went in with my sisters and my husband. I was prepared for it all! (sic)"
