The daughter of Bob Geldof was found dead from a heroin overdose at her home in Wrotham, Kent on 7 April 2014 at the age of 25.
Police had launched an inquiry last year into who had sold Peaches, a mother of two, the batch of heroin that killed her.
But the investigation was officially closed this week after police said they had "exhausted all lines of enquiry" and had not discovered the identity of the dealer.
Det Supt Paul Fotheringham told BBC News that if further witnesses came forward or information was received the case could be reviewed again. He said: "I would like to take this opportunity to pay tribute to Peaches' family who have supported our inquiries during what has been a difficult time."
Peaches was discovered dead in the the bedroom of the family home by husband Thomas Cohen. She had been looking after their one-year-old son Astala at the time, while Thomas had been away with their younger child, Phaedra.
Thomas said at the time: "My beloved wife Peaches was adored by myself and her two sons Astala and Phaedra. I shall bring them up with their mother in their hearts everyday. We shall love her forever."
Peaches' life in pictures:
Copyright: Rex Features Dennis Stone
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