Peaches Geldof died of a heroin overdose, echoing the death of her mother which had haunted her, it has been reported.
Toxicology reports at her inquest will confirm her death was as a result of the drugs overdose, the Times said.
The TV presenter was found dead while caring for her 11-month-old son at the family home last month.
Police discovered no evidence of drugs paraphernalia in the house, leading to speculation that items may have been removed before the property was searched, the newspaper said.
Coroner Roger Hatch waited for results of the toxicology tests to determine if Ms Geldof had died of an overdose before deciding to open an inquest after a post-mortem examination failed to establish the cause of death.
The Times said the results would be announced by Detective Chief Inspector Paul Fotheringham during a brief hearing in Gravesend, Kent, today. Police used drugs sniffer dogs during the search of the house and examined the contents of rubbish bags.
Mr Hatch will adjourn the inquest until the end of July to ensure that Ms Geldof's rock singer husband Thomas Cohen, and her father Bob Geldof, the former Boomtown Rats singer and founder of Live Aid, are able to attend the full hearing.
The whereabouts of items used when smoking or injecting heroin is likely to be a focus of the investigation.
Ms Geldof's mother died from a heroin overdose in 2000. Paula Yates was found dead at her home in Notting Hill, west London, having taken an accidental overdose while alone with Ms Geldof's sister Tiger Lily, then aged 4.
Hours before she was found dead Peaches posted a photograph of herself and her mother on the internet.
Ms Geldof, who also worked as a columnist, model and DJ, was looking after her youngest son Phaedra on her own when she was found dead at the detached home in Wrotham, Kent, on April 7.
The alarm was raised by Mr Cohen, 23, who had spent the previous night away with their eldest son Astala, aged 23 months. He asked a friend to visit the family house when he could not contact his wife.
Ms Geldof had a long history of drug use, including reports that she had to be revived after an overdose in 2008.
The inquest of her friend Freddy McConnel, 18, who died of a drugs overdose in 2011, heard that he had written in his diary a few months earlier: "Peaches is coming overlater and I am going to inject for the first time. Perhaps I will die. I hope I don't."
In May 2008, Ms Geldof was questioned by police but not charged after being seen offering a drug pusher up to 190 ($372). Friends said she had stopped using drugs before the birth of her children.
There was speculation that she might have accidentally overdosed because her body was not as tolerant to the quantities of heroin she had previously taken, the Times report said.
In her final interview, Ms Geldof said having her sons had helped her to overcome much of the damage caused by the loss of her mother.
"Now that I am a mum I can correct those awful parts of my childhood and it's a really healing process," she said.
"Before, I was not at peace with myself about it because I was just traumatised. That's why I was living a chaotic lifestyle."
Meanwhile, Mr Geldof is engaged to his girlfriend French actress Jeanne Marine. The couple have been together for 18 years.