"There was recent use of heroin and the levels identified were likely to have played a role in her death," Detective Chief Inspector Paul Fotheringham of the Kent and Essex Serious Crime Directorate said.
On April 7, the 25-year-old was found by her husband after visiting his parents' home.
"Thomas entered the property and went upstairs thinking that Peaches may have been sleeping," Fotheringham said. "Thomas then located Peaches in a spare bedroom and it was obvious to him that she was deceased."
"She was located on the edge of a bed with one leg hanging down to the floor with the other leg tucked underneath her; she was slumped forward across the bed," Fotheringham added.
Geldof had been in contact with friends and family throughout the weekend, Fotheringham said.
"All of the friends and family who had contact with Peaches during this period describe how she seemed her normal self and was making plans for the future, including booking a family outing for her sons the following weekend," Fotheringham said. "There was no cause for any concern."
Her autopsy was inconclusive, prompting further toxicology tests.
Geldof had admitted to previously taking drugs, but said that she had quit. She leaves behind her husband and two young sons.
The Associated Press contributed to this report.