The little girl was born at Cedars-Sinai Medical Center in Los Angeles.
Kardashian, 32, was not due to give birth until early July (13) but sources suggest both mother and baby are in good health.
The newborn's father reportedly pulled out of a launch party for his new album, Yeezus, on Friday night (14Jul13) when his girlfriend started having contractions.
Insiders claim he was present throughout the delivery.
West's rapper friend Nas took to Twitter.com to react to the happy news, writing, "Congrats (sic) to Kanye for the birth of his daughter today... To my bros w/ (with) daughters!" while hip-hop mogul Russell Simmons added, "There is no greater gift in life than a child's laughter! Congrats to Kim and Kanye."