Geldof, 25, a media and fashion personality in her own right and a mother of two young children, was found dead at her home in Wrotham, Kent, in southern England, on Monday.
Kent Police said they were treating it as a "non-suspicious but unexplained sudden death" but added investigations would continue following the inconclusive post-mortem.
"The result of a toxicology report can take several weeks," police said in a statement.
When these results are known a coroner will decide whether there needs to be an inquest, an official inquiry held in Britain when someone dies unexpectedly.
Peaches was the daughter of television presenter Paula Yates and Bob Geldof, the Irish singer who rose to prominence as the leader of the 1970s-1980s band the Boomtown Rats, and later organised the charity Band Aid and the Live Aid concerts to raise money for famine relief in Ethiopia.
Bob Geldof said the loss of Peaches, the latest untimely death to befall the family, had left them "beyond pain".
Peaches was only 11 when she and her two sisters, Pixie and Fifi Trixibelle, lost their mother.
Yates was married to Geldof from 1986 to 1996 but left him for Australian rock star Michael Hutchence, who committed suicide in 1997. Yates died three years later from a heroin overdose, aged 41.
After Yates's death, Geldof brought up Tiger Lily, Yates's daughter with Hutchence, alongside her three half-sisters.
Making an early debut in the London glamour and society scene, Peaches wrote articles for British national newspapers from the age of 14, and was often seen partying and clubbing in London's vibrant night scene.
After becoming a mother she left the party scene behind and at the time of her death was a columnist for the Mother & Baby magazine. In her last column, under the headline "Being a mum is the best thing in my life", she wrote she was "happier than ever".
"Before having two fat little cherubs under two ... I lived a life of wanton wanderlust," she said. "With fun-loving friends from Los Angeles to London, I was lost in a haze of youth and no responsibilities."
But, she had become bored of her previous lifestyle but said motherhood had initially left her "friendless" and "alienated and abandoned", she wrote.
"Now, with a new-found group of mummy mates, both locally and online ... I'm happier than ever. Right now life is good. And being a mum is the best part of it," she said.
Peaches' last Twitter post, on Sunday, was a photograph of herself and her mother.
"My beloved wife Peaches was adored by myself and her two sons ... I shall bring them up with their mother in their hearts every day. We shall love her forever," her husband, rock musician Thomas Cohen said after her death.
