The 7-pound, 14-ounce baby girl was born at Cedars Sinai Medical Center in Los Angeles.
The baby is Kardashian's second child with her longtime boyfriend, Scott Disick. They have a 2-year-old son named Mason.
Proud aunt Kim Kardashian wrote on her website that the family was thrilled to finally meet the newborn.
"She is absolutely perfect! I am so excited to be an aunt again and can't wait to spoil little Penelope," she wrote.
KABC-TV Los Angeles, CA contributed to this report.