The Real Housewives of Beverly Hills star entered rehab last December amid reports of an addiction problem.
Richards, who is Paris Hilton's aunt, spoke to host Andy Cohen on the third reunion episode of the series, saying: "I'm an alcoholic.
"I have so much guilt and shame for my behaviour and what I did. And then I drank to cover the guilt and shame."
She added: "It's been a problem long enough that I can say that I've struggled with it. I'm a person that has done it and relapsed and done it. But at least I'm trying.
"I felt off. I just didn't like me anymore and I couldn't look at myself in the mirror anymore."
Richards said: "When I first started the season I was still not drinking and you could see my confidence level.
"Then you could see just from my behaviour when I lost my confidence and started drinking.
"I could not watch the show when I saw that behaviour coming out of myself because I was so ashamed of what I'd done."
Richards's sister Kyle said that her sibling was "doing well" during her stint in rehab and following her release the reality star said that she felt "phenomenal".
Watch Kim Richards talk about her stint in rehab below (US Only):