The couple - who have known each other 1999 during Ozzfest, a tour organised by her father Ozzy - were said to be "very happy together", according to a secret source.
Last year, Osbourne shared that her battle with addiction had "robbed" her of much of life's milestones, such as having children.
She said: "I feel very behind. As a woman, I would have loved to be married and have children by now. My brother [Jack] has three daughters and I would have loved to have kids by now, but that wasn't what was in the cards for me yet."
However, the star admitted that she "would have been no kind of mother at all because I was that crazy addict that was like, 'Oh yeah, I'll stop doing drugs when I get pregnant because I have to.' Like, that's insane that I would ever even think that."
In April 2021, after four years sober, Osbourne shared that she had relapsed but was "back on track".
She said: "This is a little hard for me to talk about, but I've always promised you that I will always be honest with you about where I'm at and what's going on in my road to recovery. I relapsed. Not proud of it, but I am back on track."