Kim Kardashian and Kanye West's baby arrived five weeks early on Saturday.
The little girl - who weighted just under five pounds - is said to be the spitting image of the Keeping Up With The Kardashians star.
A source told The Sun: "She has dark hair and looks just like her mum."
No name has been revealed so far, but it's thought the pair will choose a moniker beginning with the letter K.
Donda - the name of Kanye's late mum - could also be a possibility.
The new addition to the Kardashian family was born at around 1.30am on Saturday at LA's Cedars Sinai Hospital.
Kim, 32, and 36-year-old Kanye were reportedly originally given 12th July as the due date.
Rapper Kanye skipped his own album listening party to rush to Kim's side during the birth, which saw the baby delivered naturally and without any complications.
Kim has been visited by numerous friends and family at her private birthing suite and her loved ones have already started gushing about the baby girl on Twitter.
The reality star's younger sister Khloe wrote on Twitter: "I can not even begin 2describe the miracle that is now apart of our family. Mommy/baby are healthy &resting. We appreciate all of the love."
She added: "More info will come when the time is right! Thank you all for understanding! We love you all dearly! Overwhelmed with love right now."
And Kim's mum and manager Kris Jenner tweeted yesterday: "HAPPY FATHERS DAY @kanyewest !!!!!!"
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