She captioned a series of images of her late pooch with a heartfelt tribute.
It read: “In Loving Memory of My Sweet Norman.
“I still remember the day I brought you home. I had never loved anything so much. I always wanted an Italian Greyhound growing up, but my mommy never let me have one. Then, right after I turned 17, I got you for Christmas, and it was the best gift I could have ever received.”
Jenner, who is dating 29-year-old actor Timothee Chalamet, “tried to prepare” herself for Norman’s death as he was getting older.
And she is delighted that her children – daughter Stormi, 7, and son Aire, 3, whom she has with her ex-partner, 34-year-old rapper-and-singer Travis Scott – got to meet the dog.
The Kylie Cosmetics founder said: “Normy, you filled my life and so many others with pure joy.
“Almost 13 years old, and yet I know I’ll remember you far longer than the time we got to share. I wish I wasn’t writing this post.
“I knew you were getting older, and I tried to prepare myself, but it’s hard losing you Norm. It makes me happy knowing my kids got to meet you and love you.
“My sweet Normyyyy. My heart aches for you. Rest in peace, my precious Normandle. I love you forever.”