"We are incredibly grateful to our surrogate who made our dreams come true with the greatest gift one could give and to our wonderful doctors and nurses for their special care," Kardashian West wrote.
The baby joins older siblings North, 4, and Saint, 2. No name has been announced for the newest member of the family as of yet.
The couple kept their expectant parent status quiet for awhile, refusing to confirm a baby was on its way despite published reports.
But in September, Kardashian West confirmed the news in a clip from Season 14 of her family's E! series "Keeping Up with the Kardashians."
In the promo, the reality star is seen on a video call with her sister, Khloé Kardashian.
"What happens every time I say, 'Guess what?'" Kim says to her sister.
"The person's pregnant?" Khloé asks before Kim announces, "We're having a baby!"
Kardashian-West had a pink-themed baby shower in November
and has been very open about the complications she suffered from her pregnancies.
When she was pregnant with North, she had pre-eclampsia, a complication characterized by high blood pressure. And in both pregnancies, she had placenta accreta, which occurs when the placenta attaches too deeply in the uterine wall. Kardashian West has since been open about her willingness to conceive via surrogate.
Last season on the show, Kardashian-West said, "I want my kids to have siblings, but the doctors don't feel like it's safe for me."
The last few months has been nothing but baby news for the superstar Kardashian-Jenner reality show family.
In September, CNN confirmed that Kylie Jenner was pregnant
and in December Khloé Kardashian confirmed
that she and her NBA player boyfriend Tristan Thompson were expecting.
Jenner has been keeping a low profile and has not publicly discussed her pregnancy, nor has her rapper boyfriend, Travis Scott.