Minnelli and her half-sister appear to have reconciled after falling out over a book written by Luft more than a year ago.
The singer and actress Liza Minnelli has left hospital in Florida after a three-week battle with a potentially fatal virus.
Doctors say it will be several months before she recovers fully.
The Oscar-winning star of the film Cabaret had been suffering from viral encephalitis which can be deadly.
The 54-year-old singer left the clinic with her half-sister Lorna Luft.
"I feel wonderful," she said.
She added: "I'm with my sister, and I've never felt better in my life."
Minnelli's publicist, Michael Hartman, said she was looking forward to being back at home.
Concern from her fans had pulled her through the ordeal and she wished to thank them for their prayers and their love, Hartman added.
Family reconciliation
Minnelli and her half-sister appear to have reconciled after falling out over a book written by Luft more than a year ago.
"I'm so lucky that I'm here now and Lorna and I are so lucky to be together here today," Minnelli shouted before disappearing into her rented home.
"My sister is the best," Luft said.
Doctors have appealed for Minnelli to be left in peace as she tries to recover.
"Although the condition is now under control, due to the initial severity of viral encephalitis, it will be several months before Ms. Minnelli is completely well," Dr Maurice Hanson said in a statement.
Paramedics were summoned to Minnelli's Fort Lauderdale home on 8 October after her chauffeur found the singer unconscious.
Initial reports speculated that she had suffered a stroke.