Deputy Director of Public Prosecution Eva-Marie Persson took the decision to "discontinue the investigation regarding Julian Assange", the Swedish Prosecution Authority said.
"The reason for this decision is that the evidence has weakened considerably due to the long period of time that has elapsed since the events in question," it added.
Ms Persson said: "I would like to emphasise that the injured party has submitted a credible and reliable version of events.
"Her statements have been coherent, extensive and detailed; however, my overall assessment is that the evidential situation has been weakened to such an extent that that there is no longer any reason to continue the investigation."
The prosecutors said the decision had been taken after interviews with seven witnesses in the case.