Kim Kardashian's a mum

Kim Kardashian, 32, gave birth to her first child with boyfriend Kayne West, 36, on Saturday morning.

A source confirmed to People magazine that the couple have a daughter. 

Kim gave birth five weeks early at Cedars-Sinai Medical Center in West Hollywood, California, and Kayne was by her side during the delivery. 

"I'm so excited we're having a girl," Kim said on a recent episode of Keeping Up with the Kardashians, when she learned the sex of her baby. "Who doesn't want a girl? I think they are the best. I know that's really what Kanye has always wanted – he wanted a little girl."

Another source reveals: "She started to feel sick late last night [Friday] and was having contractions.

Meanwhile, a hospital source tells Us magazine that the family is enjoying their special time together: "They're all doing great and amazing."

Great news for the star, who'd had a tough last trimester, including appendicitis (pictured above): "Getting appendicitis while pregnant is not fun. It's not easy. It's gonna be really tough to go through."

Congratulations Kim & Kanye!