Their daughter was born a month ahead of her due date.
The reality TV star is reported to have been admitted earlier this morning to the famous Cedars-Sinai Medical Centre in Beverly Hills - the popular choice for celebs wanting a five star birth, including Britney Spears, Victoria Beckham and Jessica Simpson.
Hours later Kim, 32, gave birth to her baby girl.
Rapper Kanye West, 36, and her formidable mother Kris Jenner were reportedly at her side.
Both mother and child are believed to be in good health - despite the baby's early arrival. Her due date was July 11.
There has been no hint yet of the name the couple have chosen - but see below for our top choices.
The couple announced the pregnancy in December.
Kardashian has been married twice before - to musician Damon Thomas in her 20s and most recently to basketball player Kris Humphries.
The birth of the couple's first child comes just weeks after Kim had a baby shower with over 50 guests and lavish presents.
In the first episode of the eighth season of the family's reality show, Keeping Up With The Kardashians, Kim - and her fans - discovered that she was having a baby girl.
Kim and her K-themed sisters Kourtney and Khloe and mum Kris all crowded in to look at the scan while the doctor told them 'I don't see any pee-pees'.
So what's the betting Kim and Kanye's daughter's name will being with a K?
Kimye? Karice? Kuimme? Kimberley? Kalamity? Kandy? Karrot? Karole? Karnation?
Check out our baby name generator for some seriously silly suggestions. You can even search by girl names and the letter K.
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