"Over the last six years, I have been dealing with a sex addiction," Osbourne said in a statement to ABC News, adding, "I have gone into intense therapy."
The statement also confirmed that Osbourne had had a years-long affair with his longtime hair colorist, Michelle Pugh.
She told her side of the story in a new interview with People that will be published later this week.
Pugh said she doesn't believe Osbourne is a sex addict, noting that she worked with him for a year before things turned physical. She maintained that her relationship with the Rock and Roll Hall of Famer "felt like an old-fashioned romance" and that he courted her.
"When I say he gave me the greatest love of my life, I mean it," she added.
In addition, Pugh said that Osbourne didn't act like a rock star with her, describing him as a "really nice, sweet, funny and cool guy." She also claimed that the singer "asked me not to see anyone else. We had a very real relationship."
Osbourne's statement to ABC News also addressed Pugh's claims, saying, "I'm sorry if Ms. Pugh took our sexual relationship out of context."
The note also extended an apology to other women with whom Osbourne apparently had sex, adding, "I’d also like to apologize to the other women I have been having sexual relationships with. Out of bad comes good."
"I am mortified at what my behavior has done to my family," the statement from Osbourne continued. "I thank God that my incredible wife is at my side to support me.”