Patrick Lovato, the 20-year-old singer's estranged dad, died of cancer this month at the age of 54.
"Today I put my Daddy to rest...hardest thing I've ever done," Demi tweeted Saturday.
"But I know great things will come of this," she added with the hashtag LovatoTreatmentScholarship.
"There's an overwhelming sense of peace knowing my dad is no longer battling his demons anymore and that makes me so happy," she said via Twitter.
Demi talked about the scholarship last week on "Good Morning America," UsMagazine.com said, adding the fund will help those in need pay for expenses at the rehab facility Cast Recovery.
"I'm a firm believer that everything happens for a reason," Demi said on "GMA." "My father dealt with mental illnesses and he wasn't able to function in society and that happens to a lot of people."