Kent Police said officers are continuing to investigate the circumstances around the 25-year-old's death and a toxicology report could take several weeks.
The body of the mother-of-two was found at her home in Wrotham, Kent, on Monday and police have said her death is being treated as a "non-suspicious, unexplained sudden death".
Ms Geldof's body was found on Monday afternoon after officers were called "following a report of concern for the welfare of a woman".
A Kent County Council spokesman said yesterday that her body had been transferred to Darent Valley Hospital in Dartford for a post-mortem examination to take place.
In a statement today, Kent Police said: "A post-mortem examination held on Wednesday April 9 following the death of Peaches Geldof has proved inconclusive pending the result of toxicology analysis.
"Officers were called to the 25-year-old's home in Fairseat Lane, Wrotham, at 1.35pm on Monday April 7 2014. Peaches was pronounced dead at the scene.
"This is being treated as a non-suspicious, unexplained sudden death.
"Officers continue to investigate the circumstances surrounding the death in order to compile a report for the coroner.
"The result of a toxicology report can take several weeks."
A coroner is expected to open an inquest into Ms Geldof's death following the results of the initial post-mortem examination.
Her father, Bob Geldof, and other members of the family led the tributes which flooded in after the death.
In a touching tribute signed by the Live Aid organiser, his partner Jeanne Marine, and Ms Geldof's sisters Fifi Trixibelle, Pixie and Tiger, they said the family was "beyond pain", writing: "She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us."
Ms Geldof's husband, musician Tom Cohen, with whom she had two young sons, said his wife was adored by him and their two sons Astala, 23 months, and 11-month-old Phaedra, who he would bring up "with their mother in their hearts every day".
Ms Geldof's elder sister Fifi yesterday posted a picture on Instagram of the two of them together when they were children, writing: ''My beautiful baby sister... Gone but never forgotten. I love you Peaches x.''
Ms Geldof was just 11 when her mother, TV presenter Paula Yates, died from an accidental heroin overdose in 2000, aged 41.
She married US musician Max Drummey in Las Vegas in 2008, when she was 19, but the couple split amicably in February 2009 before divorcing in 2011.
She married Cohen, lead singer of south-east London band Scum, in September 2012 at the church in Davington, Kent, where her parents married 26 years earlier. It was also where her mother's funeral was held.
A prolific tweeter, the final message she sent on Sunday was a picture of herself as a child with her mother, with the message "Me and my mum".
In a column for Mother & Baby magazine, she wrote how she was now "happier than ever" after becoming a mother.