The 62-year-old matriarch's youngest child welcomed a daughter - her first baby with boyfriend Travis Scott - into the world last week and Kris thinks the 20-year-old star has taken to her new role very well.
She gushed: ''She's amazing. An amazing mom.''
Kylie never confirmed reports she was expecting a baby, but after announcing her little girl's birth, the 'Keeping Up With the Kardashians' star shared an 11-minute video montage of moments from her pregnancy and labour.
And the emotional short film left Kris ''bawling''.
She told People magazine: ''I was bawling! I was crying so hard, especially at the end. And I still cried.''
As well as Kylie's new baby, Kim Kardashian West and her husband Kanye West welcomed their third child, daughter Chicago, into the world last month, and Khloe Kardashian is expecting her first child with partner Tristan Thompson, and Kris couldn't be happier.
She said: ''It's a whole 'nother dimension of love and family, and feeling so lucky to be where we are today. It's really an exciting time.
''Any mom just wants her family to be happy, healthy, peaceful, joyful and that's my joy. They're my heart!''
The family momager is now looking forward to play dates between her grandchildren, which also includes son Rob Kardashian and his ex-fiancee Blac Chyna's daughter Dream, 14 months, Kourtney Kardashian and former boyfriend Scott Disick's three kids, Mason, eight, Penelope, five, and Reign, three, and Kim and Kanye's older children, North, four, and Saint, two.
She said: ''That's what makes it so fun.''
Meanwhile, Kim is also looking forward to Chicago and Kylie's baby growing up as ''besties''.
She wrote on her website: ''Mommy Kylie!!! You did it!! I'm so incredibly proud of the woman you have grown up to be and I know that you are going to be the best mom to your new baby girl!
''Our girls are two weeks apart and I can't wait for them to be besties! I am so proud that you do what you want to do and live your life the way you want, you will pass down all of those amazing qualities to your baby girl. You were made to be a mom! I love you!''
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