"Peaches has died. We are beyond pain," he wrote. "She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us.
"Writing 'was' destroys me afresh," he added. "What a beautiful child. How is this possible that we will not see her again? How is that bearable?"
Authorities have described Geldof's death as "unexplained and sudden," though they have no reason to believe she died under suspicious circumstances.
In her final column for a British parenting magazine, published posthumously on Tuesday, Geldof said she had abandoned her partying ways for a stable home life with her husband, Thomas Cohen, and two children, Astala and Phaedra.
Geldof's mother, British TV presenter Paula Yates, died of a heroin overdose when Peaches was 11.
Here's the full statement from Kent Police:
A postmortem examination held on Wednesday 9 April 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, 7 April 2014. Peaches was pronounced dead at the scene. 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.