Eva-Marie Persson, Sweden's deputy director of public prosecutions announced the decision at a news conference in Stockholm on Monday morning.
If convicted in Sweden, Assange could face a prison sentence of up to four years.
Swedish prosecutors filed preliminary charges - a step short of formal charges - and issued a European arrest warrant against Mr Assange after he visited the country in 2010.
- April 11, 2019: London police arrest Assange at the Ecuadorian embassy for breaching bail conditions in 2012, as well as on behalf of US authorities, shortly after Ecuador's government withdrew his asylum status. The authorities care so little about violence against women that they manipulate rape allegations at will. [Assange] has made it clear he is available for questioning by the Swedish authorities, in Britain or via Skype. Their chance to pursue charges in the case will expire next summer, under Sweden's statute of limitations. Assange was arrested by British police on April 11 and later sentenced to 50 weeks in a British prison for skipping bail.
Assange's supporters cast him as a dissident facing the wrath of a superpower over one of the largest compromises of classified information in USA history.
Persson said the investigation would end after that if no charges are filed against Assange.
"I am deeply concerned about the Swedish authorities reopening the investigation in fear that it will result in Julian having to go to Sweden as they have a record of meekly obeying United States extradition requests ..."
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The decision to reopen the investigation poses the question of whether Assange will be moved to Sweden or to the United States.
She added that while there is a risk the case may cut close to the statute of limitations deadline, "there is also a chance that we will be able to get him extradited before August 17 next year". Manning has said that she wanted to expose what she considered to be the US military's disregard for how the Iraq War was affecting civilians, and that she was motivated "out of a love for my country".
She said: "No rape victim should have to wait nine years to see justice be served".
Assange's asylum in the Ecuadorean embassy in London prevented him from being surrendered to Swedish prosecutors.
- February 5, 2016: Assange claims "total vindication" as the U.N. Working Group on Arbitrary Detention finds that he has been unlawfully detained and recommends he be immediately freed and given compensation.
Mr Assange, an Australian citizen, is now being held in Belmarsh prison serving a 50-week sentence for skipping bail in 2012.
"In the event of a conflict between a European Arrest Warrant and a request for extradition from the US, UK authorities will decide on the order of priority". Assange denied the claims, saying the sex was consensual.
Hrafnsson also said in a statement that there had been "political pressure" on Sweden to reopen the case. Sweden discontinued the investigation in 2017 because they said they were unable to advance the case while Assange was holed up at the embassy.