Kardashian, who is also mom to 2-year-old son Mason with boyfriend Scott Disick, told the magazine that she was entirely unprepared for the amount of love she would feel for her newborn daughter.
"Nothing could prepare me for how hard I fell in love with her!" she said.
Kardashian gave birth to 7-pound-14-ounce Penelope Scotland Disick in Los Angeles on July 8.
Dad is noticeably absent from the magazine's cover, which has Kardashian and her two children dressed in white. But inside the new issue, Disick, 29, and Kardashian, 33, open up about Penelope's delivery - with the whole Kardashian-Jenner clan present - Mason adjusting to life as a big brother, Kardashian's push present and why Disick still hasn't changed a single diaper.
After Penelope's birth, Kardashian's famous sisters gushed on Twitter about their new niece.
Kim Kardashian wrote: "She is absolutely perfect! I am so excited to be an aunt again and can't wait to spoil little Penelope. I know Mason is going to be the best big brother in the whole world. Congratulations Kourtney and Scott. Xo"
Khloe Kardashian wrote an entire blog: "The entire family is literally exploding with joy and have not stopped fawning over our new little girl. And Mason is already loving being a big brother!"