has given birth to a baby girl ... TMZ has learned.
Source close to KK tell TMZ ... it was a NATURAL CHILD BIRTH. She started having contractions Friday night and went into full labor early Saturday AM.
Our sources tell us the baby and Kim are both in good health. We're told Kim delivered the baby at Cedars-Sinai Medical Center this morning ... 5 weeks early.
It is the first child for Kim and Kanye.
Watch this space for EXCLUSIVE photos.
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