The Talk has been off air while CBS investigated the incident and has now announced Sharon has left the programme.
It said her behaviour during the 10 March episode “did not align with our values for a respectful workplace”.
In a statement obtained by the PA news agency, it said: “Sharon Osbourne has decided to leave The Talk.
“The events of the March 10 broadcast were upsetting to everyone involved, including the audience watching at home.
“As part of our review, we concluded that Sharon’s behaviour toward her co-hosts during the March 10 episode did not align with our values for a respectful workplace.”
Responding to Sharon’s claims she had been set up by producers, CBS said: “We also did not find any evidence that CBS executives orchestrated the discussion or blindsided any of the hosts.”
However, CBS said it acknowledges the network, studio teams and producers are “accountable for what happened during that broadcast” because “it was clear the co-hosts were not properly prepared by the staff for a complex and sensitive discussion involving race”.
CBS said during The Talk’s hiatus it will coordinate “workshops, listening sessions and training about equity, inclusion and cultural awareness for the hosts, producers and crew”.
It added: “Going forward, we are identifying plans to enhance the producing staff and producing procedures to better serve the hosts, the production and, ultimately, our viewers.”
The Talk is set to return to US screens on Monday 12 April.
The former X Factor judge has been contacted for comment.
Sharon’s future on The Talk was thrown into doubt after she clashed with co-host Sheryl Underwood, during a discussion about Piers’ comments on Meghan’s recent interview with Oprah Winfrey.
He was criticised for saying he does not believe the duchess after she revealed she had suffered with her mental health and had suicidal thoughts.
During a heated discussion, Sharon said: “I feel even like I’m about to be put in the electric chair because I have a friend who many people think is a racist so that makes me a racist.”
Sharon confronted co-host Sheryl, who is Black, and told her “don’t try and cry, because if anyone should be crying, it should be me”.
She added: “You tell me where you have heard him say, educate me, tell me when you have heard him say racist things.
“Educate me. Tell me.”
Sheryl said it was “not the exact words of racism” but “the implication and the reaction to it, to not want to address that because she is a Black woman and to try to dismiss it or to make it seem less than what it is, that’s what makes it racist”.
Sharon, wife of rocker Ozzy Osbourne, later said she was “truly sorry” if she caused offence with her comments.
She gave an interview to Entertainment Tonight and alleged she had not been sufficiently prepared for the conversation by producers.
Sharon said her co-hosts “had preparation, they had written questions for them” but she was only approached eight minutes before filming began and was asked if she was OK with discussing Piers.
She told ET she felt she had been “set up,” adding: “My anger was like, I cannot believe this, I’m your sacrificial lamb.”