The 24-year-old singer recently celebrated the five-year anniversary of her own sobriety, following drug and alcohol issues, and Demi is pleased Miley has also decided to give up using narcotics.
The brunette beauty - who has previously struggled with eating problems and bipolar disorder, too - told The Hollywood Reporter: ''I am really proud of Miley. I think that it helps people to know that there are people in the spotlight that have challenges, that are faced with very stressful lives.
''I think it helps to know that recovery is possible and it's something that is so important to certain people like myself.''
Meanwhile, Miley recently admitted she has more ''energy'' since she stopped smoking marijuana.
The 24-year-old singer announced during an interview published earlier this month that she was three weeks clean from smoking the addictive drug.
And speaking more recently, Miley said it's ''weird'' how much her life has already changed just from being clean for ''nine or 10 weeks''.
The 'Malibu' hitmaker said: ''At [the time of the interview] it was like three weeks, now it's like nine weeks or 10 weeks or something. Everyone always hits me up. A lot of people have reached out to me and [asked if I want help]. And I'm like, 'No, when I want something, I can do it.' Anything that I want to do, if I want to stop or start something, I can do anything. I just decided not to anymore and now it's easy for me.
''It's very weird. I've got a lot of energy. I'm a very obsessive person, which I need to work on, but also it helps in my position to be a little obsessive because then I can really get things done and make sure it's perfect.''