Investigations into the sexual assault charges stemmed back to 2010 when the 48-year-old Assange, during his stay in Stockholm, allegedly raped and abused two women. Assange is now serving 50 weeks in London's Belmarsh Prison for skipping bail in 2012.
"My assessment is that all investigative measures that can be taken have been taken", Deputy Chief Prosecutor Eva-Marie Persson told reporters in Stockholm.
The 48-year-old Australian is the figurehead of the whistleblowing website that exposed government secrets worldwide, notably the explosive leak of United States military and diplomatic files.
Still, Persson said her statements "have been coherent, extensive and detailed". In 2012, the Australian publisher and activist-who has denied the rape allegation-was granted political asylum by Ecuador and took up residence in the country's embassy in London to avoid being extradited to Sweden.
Mr Assange first sought refuge at the embassy after being accused of the sexual assault charges.
A spokesman for Assange's legal team said: "From the outset of Sweden's preliminary investigation, Julian Assange's expressed concern has been that waiting in the wings was a United States extradition request that would be unstoppable from Sweden-and result in his spending the rest of his life in a USA prison".
The decision, which can be appealed to the attorney general, removes one possible hurdle to Assange's extradition to the USA, where he's wanted for endangering national security by conspiring to obtain and disclose classified information. He was sentenced in May to 50 weeks in prison for jumping bail in 2012.
Assange's Swedish lawyer, Per Samuelson, said as far as he was aware, his British lawyers had not yet been able to contact Assange in jail to inform him of the Swedish decision.
Welcoming the Swedish prosecutor's decision, WikiLeaks editor-in-chief Kristinn Hrafnsson said, "Let us now focus on the threat Mr. Assange has been warning about for years: the belligerent prosecution of the United States and the threat it poses to the First Amendment". She said she had refused to have unprotected sex with him before the alleged incident. This follows a June decision by a Swedish court that Assange should not be detained. After Assange's removal from the embassy in spring 2019, the case was reopened at the request of the counsel for the injured party in Sweden.
USA authorities accuse Assange of scheming with former Army intelligence analyst Chelsea Manning to crack a password that provided access to classified material on a government computer.