According to well-informed website US Weekly, the reality TV star gave birth in a LA hospital after going into labour this morning.
The website reports that the birth came five weeks early, with the due date scheduled for 11 July. Both her mother Kris Jenner and West were reported to be at her side.
Kardashian had previously confirmed that she and West were expecting a girl. While the music-maker has been celebrating the launch of his new album in Europe and New York in recent days, the reality star has been confined to LA during the last stages of her pregnancy.
West had been due to attend a listening party for his new album in New York last night, but failed to attend, sparking rumours that baby was on the way.
While he has been busy working, the R&B star has been waxing lyrical about forthcoming parenthood, telling the New York Times: "I would do anything to protect my child or my child's mother."
According to the Daily Mail, Kardashian had booked a luxury birthing suite at the famous Cedars-Sinai hospital in Los Angeles, which previously played host to expectant mothers Victoria Beckham, Jessica Simpson and Britney Spears.
Pictures: Kim Kardashian's changing style...
Kim Kardashian Style Evolution
2007(01 of28)
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Kim Kardashian walks the runway. (credit:Getty Images)
2008(02 of28)
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Kim Kardashian wears wide leg trousers and black vest. (credit:Getty Images)
2008(03 of28)
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Kim Kardashian wears a yellow top and shoes with jeans. (credit:Getty Images)
2008(04 of28)
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Kim Kardashian wears a green print dress. (credit:Getty Images)
2008(05 of28)
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TV Personnality Kim Kardashian wears a printer top over jeans. (credit:Getty Images)
2009(06 of28)
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Kim Kardashian poses wearing a white waistcoat and trousers. (credit:Getty Images)
2009(07 of28)
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Kim Kardashian wears denim shorts and a zebra print jacket. (credit:Getty Images)
2009(08 of28)
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Kim Kardashian wearing a pink animal print dress. (credit:Getty Images)
2010(09 of28)
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Kim Kardashian walks the runway at the Heart Truth Fall 2010 Fashion Show. (credit:Getty Images)
2010(10 of28)
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Kim Kardashian and her mother Kris Jenner are seen in Italy. Kim wears a purple playsuit. (credit:Getty Images)
2010(11 of28)
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Khloe and Kim Kardashian a basketball match. Kim wears an all black outfit with a fur sleeve. (credit:Getty Images)
2010(12 of28)
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Kim Kardashian attends Heidi Klum's 2010 Halloween Party. (credit:Getty Images)
2010(13 of28)
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Kim Kardashian promotes her new book Kardashian Konfidential wearing a statement necklace. (credit:Getty Images)
2011(14 of28)
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Kardashian attends adds attitude to her dainty floral skirt with black jacket, tights and boots. (credit:Getty Images)
2011(15 of28)
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Kim Kardashian wears a gold number with Louboutin heels at the Grammy Awards. (credit:Getty Images)
2011(16 of28)
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Kim Kardashian wears a black fishtail gown. (credit:Getty Images)
2011(17 of28)
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Kim Kardashian wearing wet-look leggings and cream jacket. (credit:Getty Images)
2011(18 of28)
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Kim Kardashian wears a black playsuit with embellished shoulder detail. (credit:Getty Images)
2011(19 of28)
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Kim Kardashian wears a waterfall cream jacket with thigh-high boots. (credit:Getty Images)
2011(20 of28)
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Kim and Kourtney Kardashian in New York. (credit:Getty Images)
2011(21 of28)
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Kim Kardashian attends the Vera Wang Spring 2012 fashion show wearing blue dress with red lips. (credit:Getty Images)
2011(22 of28)
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Kim Kardashian wears a short gold dress to a birthday party. (credit:Getty Images)
2012(23 of28)
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TV personality Kim Kardashian wears a silver dress. (credit:Getty Images)
2012(24 of28)
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Kim Kardashian arrives at the annual White House Correspondents' Association dinner wearing a green dress with embellished shoulder detail. (credit:Getty Images)
2012(25 of28)
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Kim Kardashian wears a figure hugging navy dress with thin straps. (credit:Getty Images)
2006(26 of28)
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Kim Kardashian arrives at launch wearing a floral print dress. (credit:Getty Images)
2012(27 of28)
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Kim Kardashian wears a floor-length yellow gown with thigh-high split. (credit:Getty Images)