The singer, 25, wrote a message to fans on her Instagram page saying she had learned addiction is "not something that disappears or fades with time" and "it is something I must continue to overcome and have not done yet".
Lovato also thanked staff at the Cedars-Sinai Medical Centre in Los Angeles, where she was taken after falling ill at her home in the Hollywood Hills on 24th July.
She added: "I want to thank God for keeping me alive and well.
"I now need time to heal and focus on my sobriety and road to recovery.
"The love you have all shown me will never be forgotten and I look forward to the day where I can say I came out on the other side. I will keep fighting."
Lovato was a child star and found fame on the TV series Barney & Friends before appearing in the Disney Channel film Camp Rock.
She has since gone on to be a multi-platinum pop star with hits such as Sorry Not Sorry, Skyscraper and Heart Attack.
Lovato has been open about her struggles with alcohol and substance abuse and in June released a song, titled Sober, in which she indicated she had relapsed after six years of sobriety.
After reports emerged that New Mexico-born Lovato had been taken to hospital, the hashtag #PrayForDemi started trending on Twitter and celebrities including Ariana Grande, Cardi B and Nick Jonas tweeted messages of support.
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