Fifi Geldof, 31, said she was first diagnosed with the mental illness at the age of 11, following the break-up of her parents, Boomtown Rats frontman Bob Geldof and television presenter Paula Yates.
Her mother died from a heroin overdose at her London home in September 2000, while sister Peaches died of a heroin overdose in April this year after losing her battle against addiction to the Class A drug.
In an interview with The Mail On Sunday - her first with a print journalist - Fifi described how she took drugs, drank heavily and began comfort eating following her mother's death, having previously being treated for clinical depression.
She said of her parents' divorce: "Their break-up was pretty horrendous. I was at that difficult pre-teen age when kids are supposed to be surly and difficult.
"He (the therapist) diagnosed me with clinical depression. I didn't say a word for the first three sessions. I just sat there staring at him."
She added: "I never expressly told my parents. Dad doesn't know. I wouldn't talk to him about it now. I don't have that relationship with my family."
Fifi, who now works in PR, said she did not have a close relationship with her mother.
But she said of her sister's death: "A piece of my heart and my soul has gone. She was my baby sister."
Fifi hit back at internet trolls following Peaches' death, saying they had ''no idea what you're talking about quite frankly''.
Later she thanked her followers who had posted messages of support.
''Thanks for your beautiful words of love and support for myself and Peaches. I appreciate it more than ever today,'' she said.
Peaches' one-year-old son Phaedra had been in the family home in Wrotham, Kent, when the former model and journalist died.
An inquest heard that police found 6.9g (0.24oz) of ''importation quality'' heroin stashed in a black cloth bag inside a cupboard over a bedroom door at the house with a purity of 61%, worth between £350 and £550.
They also discovered a syringe containing residue of heroin inside a sweet box next to the bed, and other drug paraphernalia including burnt spoons, syringes and knotted tights throughout the property.
North West Kent coroner Roger Hatch said Ms Geldof's death had been ''drugs-related'' and heroin played a part.