The TV personality has returned to the ITV talent show's judging panel, having previously quit after four series in 2007.
Speaking to various newspapers, she revealed that she decided to come back after dining with Cowell in March.
She said: "I said, 'If I suck your d**k can I get the job?' And he said, 'Of course'. It was very simple."
Cowell had fallen out with Osbourne after he spoke about her in his authorised biography. She then retaliated by saying he has "small penis syndrome".
However, she has now stated: "I only said that because he said he didn't like working with me in his book."
Osbourne has also said that she will not have any kind of rivalry with fellow judge Nicole Scherzinger, following her previous fallout with Dannii Minogue.
She said: "It is not going to happen because if anyone had done their homework they would know she was my guest at judges' homes. We have been friends for years."
On the chances of having a fashion contest with the singer, she said: "Please. All my stuff is one-of-a-kind couture, don't be ridiculous."
Sharon Osbourne recently joked that she would give Prince Charles oral sex for an official title.
The X Factor returns for its 10th series later this year.
Watch the X Factor stars discuss Sharon Osbourne's return with Digital Spy below: