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.