The tot was born five weeks early on Saturday (15.06.13) and Beyonce, whose husband Jay-Z collaborated with Kanye on the album 'Watch The Throne', took to her website to pass on her good wishes.
Over a large picture of Kim and Kanye together, Beyonce wrote: ''Congratulations Kim & Kanye. Enjoy this beautiful moment together.''
Meanwhile, Kim's close friend Jonathan Cheban revealed Kim, 32, is ''doing amazing''.
He told People.com: ''Kim is doing amazing and couldn't be happier. I'm so thrilled for her and Kanye.
''Kim was glowing.''
Kanye, 35, was in the delivery room when Kim gave birth naturally at Cedars-Sinai Medical Centre in Beverly Hills and although the couple's daughter was premature, she is in good health and weighed almost five pounds when born.
A source previously said: ''Of course, Kanye was there with Kim when she went to the hospital and had the baby. She started to feel sick late Friday and was having contractions.
''They're all doing great and amazing.''
A number of Kim's close friends including Jonathan and Brittny Gastineau were spotted visiting her in hospital carrying bouquets of pink flowers.