Kanye West and Kim Kardashian
06/15/2013 AT 04:05 PM EDT
The most eagerly awaited addition to the Kardashian clan has arrived – and she was apparently early to the party!
, 32, gave birth to her first child – a daughter
– with boyfriend Kanye West
, 36, on Saturday morning, a source confirms to PEOPLE. Her due date was widely reported to be in July.
West was by Kardashian's side for the delivery, according to sources, despite a busy travel schedule leading up to the birth.
The youngest Kardashian will already have playmates her age. Kim's big sister, Kourtney has two children with boyfriend, Scott Disick: Mason
, 3½, and Penelope
, who turns one on July 8.
"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."
West publicly broke the news
of his girlfriend's pregnancy mid-song at an Atlantic City concert the night before New Year's Eve. Kim later confirmed the news, posting on her website, "It's true!! Kanye and I are expecting a baby. We feel so blessed and lucky and wish that in addition to both of our families, his mom and my dad could be here to celebrate this special time with us."
Since announcing her pregnancy, Kim experienced some bumps in the road, including criticism
for her expectant outfit choices and a seemingly never-ending divorce from Kris Humphries – that was eventually finalized
just earlier this month.