The TV star and former fashion reporter was talking about Jolie's decision to have preventative cancer surgery on CBS show The Talk.
The 30-year-old said: "I actually do have the cancer gene."
Her mother, Sharon, also has the gene and had a double mastectomy in 2012. "My mom made all of us get tested. I agree with this 100%," said Kelly.
"I know that one day I will eventually have to do it too because if I have children, I want to be there to bring them up.
"I want to be there to support them in every way I can.
"It's something I applaud Angelina for because she's bringing attention to this, and people are now going to go out and get tested for it."
Angelina Jolie, 39, wrote an article in the New York Times to explain her decision to have both her ovaries and Fallopian tubes removed.
She has lost her mother, maternal aunt and maternal grandmother to cancer.
While neither Kelly nor her mother have suffered from ovarian or breast cancer, Sharon was diagnosed with colon cancer in 2002.
She successfully fought the disease with two surgeries which was documented in the family's reality show on MTV, The Osbournes.
After her recovery Sharon underwent genetic testing that revealed she carried BRCA1, the same gene as Angelina Jolie.
She then decided to have a double mastectomy.
Last month, Kelly Osbourne quit her role as the co-host of E!'s Fashion Police.
She had been on the show since 2011.
A statement released at the time by E! said: "Kelly Osbourne is departing E!'s Fashion Police to pursue other opportunities."
It came days after her co-star Giuliana Rancic was forced to apologise over a joke about Disney star Zendaya Coleman's hair at the Oscars.
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Kelly Osbourne has revealed, that like Angelina Jolie, she plans to have her ovaries removed.