Kim Kardashian West and Kanye West have named their new-born daughter, delivered by surrogate on Monday, Chicago West.
Kardashian West said that not carrying the child herself was "so hard", but that the couple had an instant connection with her.
West was raised in the US city Chicago.
Kardashian West carried and gave birth to her older children but was advised against getting pregnant again because of possible medical complications.
Her daughter North is now four years old and her son Saint is two.
But she suffered from pre-eclampsia and placenta accreta on those occasions.
Pre-eclampsia is a condition that usually occurs in the second half of pregnancy and can cause serious complications including seizures and death if not monitored and treated.
Placenta accreta is when the placenta attaches itself too deeply into the wall of the uterus and remains attached after childbirth.
Kardashian West, a reality TV star, said in a post on her app that "doctors said that it wasn't safe for my, or the baby's, health to carry my own".
The 37-year-old said she and her rapper husband decided to use a "gestational carrier", meaning the baby is "biologically mine and Kanye's".
The Wests on their most recent outing
She wrote: "Having a gestational carrier is definitely different, but anyone who says or thinks it's the easy way out is completely wrong.
"People assume it's better because you don't have to deal with the physical changes, pain or complications with delivery, but for me it was so hard to not carry my own child, especially after I carried North and Saint."
Kardashian West's surrogate was discussed on her reality show Keeping up with the Kardashians, but her identity was not revealed.