The baby came about a month early, as the E! reality star's due date was reported to be July 11 or thereabouts.
"Kim had her baby," a hospital source told Us. "She's five weeks early. Kim got sick last night and had the baby early. They're all doing great and amazing!"
West, whose leaked album "Yeezus" has already taken the Internet by storm, was said to have been there for the entire delivery; he reportedly canceled his Friday appearance at his record release party because his girlfriend said she was feeling "a little off."
On June 4, Kardashian finalized her divorce from Brooklyn Nets player Kris Humphries, whom she infamously filed for divorce from in October 2011 after 72 days of marriage. She confirmed the news that she was expecting a baby girl on the season premiere of her family's reality show.
"I'm so excited we're having a girl," Kim Kardashian said on the show after learning the baby's sex."Who doesn't want a girl? They are the best and I know that's really what Kanye has always wanted. He wanted a little girl."
The family celebrated Kardashian's baby shower about two weeks ago, with West making an appearance toward the end of the festivities.
The child comes amid rumors that West, who was already criticized for being absent during much of Kardashian's "painful pregnancy," had been cheating on his girlfriend with a Canadian model. Both he and Kardashian's reps shut down the allegations.
West has also said that he's embracing his role as a father in a recent interview with the New York Times.
"I would do anything to protect my child or my child's mother," he told the newspaper.
The sex tape-maker-turned-reality star/businesswoman reportedly has plans to take her baby girl on tour with West when he kicks off his concert tour in October.
Season 8 of "Keeping Up With the Kardashians" is airing on E!, with this Sunday's episode expected to show Kardashian struggling with appendicitis during the pregnancy.
The couple began dating in April 2012 after being friends for years. They made the announcement that they were expecting on Dec. 30. Though the couple have not said that they have any plans to marry, Kardashian previously said that's she's still open to tying the knot again.
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