Paramedics pronounced the 25-year-old celebrity dead at her home in southeast England on Monday. Kent Police said the toxicology report could take several weeks.
Geldof, daughter of Irish singer Bob Geldof and late TV presenter Paula Yates, was widely known in fashion and celebrity circles. She worked as a model, television presenter and fashion writer.
Although she admitted to taking drugs, she said in a 2009 interview that she had quit.
She is survived by her second husband Tom Cohen, lead singer of the defunct London punk band S.C.U.M, and two sons, 23-month-old Astala and 11-month-old Phaedra.
In a column for Mother and Baby magazine, published the day after her death, Geldof wrote that motherhood had made her "happier than ever."
"I've achieved a sort of perfect balance," she wrote. "Right now life is good. And being a mum is the best part of it."
Police are investigating her death as non-suspicious but unexplained. Detectives will give their report to a coroner, who is expected to hold an inquest.
In Britain, coroners usually hold inquests to determine the facts of unexplained, sudden or violent deaths.
The Associated Press contributed to this report.