Tweeting following the news of her daughter's decision, 62-year-old Sharon said she was "proud" of Kelly.
"".@KellyOsbourne, I am so proud of you. You can never be bought. You always wear your heart on your sleeve. #ProudToBeYourMum," Sharon Osbourne tweeted.
Dave Benett
No doubt she had learned a lesson from her mother Sharon, who famously quit NBC's America's Got Talent in 2012.
The Talk host has said that she walked away from the hit show after she discovered that the network had dropped her son, Jack Osbourne, after allegedly learning about his multiple sclerosis diagnosis.
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On Friday, Melissa posted a message on her Whosay account after Kelly's departure was confirmed.
"Kelly Osbourne is a friend and has been a wonderful part of the Fashion Policefamily. I will miss her terribly and wish her the very best in all of her future endeavors. As my mother always said, the show must go on and I plan to continue in the same spirit," Rivers wrote.
The Brit star is said to be "furious" over "racist" comments made about actress and singer Zendaya because of her dreadlocked hair.
Splash
Rancic, 39, apologised live on E! on Tuesday. But, Kelly was left horrified, and immediately tweeted saying she was "seriously questioning staying on the show."
A source close to Kelly says she had an agonising few days since Guiliana's criticism of her friend Zendaya but eventually decided she had to depart.
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"She is an intelligent, bright woman with priniciples. Those principles were at the heart of her wanting to leave."
The show is anchored by comic Kathy Griffin since the death of Joan Rivers - Kelly's close friend.
Griffin replaced the late Rivers, who died in August.
Fashion Police - which is produced by Joan's daughter Melissa - critiques stars at red carpet events.
Reuters
A spokesperson for the E! network said: "Kelly Osbourne is departing E!'s Fashion Police to pursue other opportunities, ad we would like to thank her for her many contributions to the series over the past five years, during which time the show became a hit with viewers."