The 'Keeping Up with the Kardashians' star and the rapper, who began dating almost a year and a half ago after a decade of friendship, have yet to officially comment on the birth of their daughter but Kim posted a touching message about her late father Robert Kardashian, her stepfather Bruce Jenner and Kanye on her blog on Sunday (16.06.13) to celebrate Father's Day.
She wrote: "Father's Day is always bitter sweet. Of course every year that goes by I miss my dad just as much as the last, but I am so blessed to have had two incredible dads in my life that have taught me everything I know! Thank you Bruce for always being there for me, and thank you Dad for raising me right!
"To all the fathers out there, Happy Father's Day!! And to all the baby daddy's out there, you are loved! ;) Xo"
A source previously revealed that that the 'New Slaves' hitmaker was in the delivery room when Kim gave birth naturally at Cedars-Sinai Medical Centre in Beverly Hills.
Despite being born five weeks early, the couple's daughter is in good health and weighs almost five pounds.
Another insider said: "Of course, Kanye was there with Kim when she went to the hospital and had the baby. She started to feel sick late last night [Friday] and was having contractions.
"They're all doing great and amazing."
A number of Kim's close friends including Jonathan Cheban and Brittny Gastineau were spotted visiting her in hospital carrying bouquets of pink flowers.
Kanye's friends Nas and Russell Simmons offered their congratulations on Twitter.