The inquest heard that Peaches, mum to Astala, two, and one-year-old Phaedra, was a heroin addict who had been taking the substitute drug methadone in the two and a half years before her death on April 7 this year.
Peaches started using heroin again in February this year, her husband, Thomas Cohen, told the hearing in Gravesend, saying he had witnessed her flushing drugs she had hidden in the loft of their home in Wrotham, Kent, down the toilet.
Peaches, 25, was found slumped on the bed in the spare room by Thomas, with one leg hanging down to the floor and the other tucked underneath her after she failed to answer the phone.
Musician Thomas confirmed that he had gone to stay with his parents in south east London with the couple's two sons Astala and Phaedra, and that Peaches had seemed fine when he spoke to her on several occasions over the weekend.
After failing to get hold of his wife the next day, Thomas and his mother returned to the property with Astala and found Peaches' body.
The model had been having weekly drugs tests which she had told her husband were negative but, even though he had not seen her take drugs, he became concerned that she might be.
A post-mortem examination found a puncture mark on the front of her right elbow and another at the front of her right thigh. Old puncture marks were also found on her left thigh, the inquest was told.
Police investigating Peaches' death found 'importation quality' heroin stashed in a black cloth bag inside a cupboard over a bedroom door and drugs paraphernalia in the property.
Detective Chief Inspector Paul Fotheringham, who led the investigation, told the inquest that the drugs would have been worth £350 to £550.
Mr Fotheringham said: "The black bag also contained 34 medical syringes, some were with needles and some without, some were sealed in original packaging and some contained traces of a brown coloured residue. There were also 45 packaged and sealed syringes, alcohol wipes and cotton buds."
A burnt spoon was also found under the bed where Peaches was found dead together with cotton wool, and other burnt spoons were located throughout the house.
Mr Fotheringham told the inquest that forensic scientist Emma Harris found a high level of morphine in Ms Geldof's blood, suggesting she died 'shortly after taking heroin' and that it was 'likely' the substance played a role in her death.
In her report, Dr Harris said: "Persons taking heroin on a regular basis develop a tolerance to the drug, and such individuals can use doses that would be toxic, or fatal, to people with no tolerance.
"However, tolerance to heroin and other opiate drugs appears to be lost fairly rapidly when users cease to use the drug, and deaths commonly occur in people who have previously been tolerant and have returned to using heroin."
After hearing the evidence, Mr Hatch concluded that Peaches' death was drugs-related and that heroin had played a part in her death.
Mr Hatch said: "It's said that the death of Peaches Geldof-Cohen is history repeating itself but this is not entirely so.
"By November last year she had ceased to take heroin as a result of the considerable treatment and counselling that she had received.
"This was a significant achievement for her but, for reasons we will never know, prior to her death she returned to taking heroin."