Assange, 48, had repeatedly denied the allegation.
The prosecutors said the decision had been taken after seven witnesses in the case had been interviewed.
Deputy Director of Public Prosecution, Eva-Marie Persson, said that the evidence for the allegation - which relates to an incident in 2010 - was not sufficient to prove a criminal act was committed. Persson said the case was dropped at this point because it was not possible for Britain to extradite Assange to Sweden.
She said: 'I'm holding this press conference to inform you I'm discontinuing the preliminary investigation'.
Commenting on the decision, WikiLeaks editor-in-chief Kristinn Hrafnsson underscored the need to "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".
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Gaga served as a bridesmaid at weddings, wearing a lovely pink dress that featured a slit to the left leg. The 33-year-old singer wore a black costume and hoop costume and tied her piny hair in a bun.
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Trae Young had 20 points for the Hawks , who dropped their second in a row. "I couldn't wait to be home", George told Fox Sports. Coach Doc Rivers described Leonard as day-to-day Saturday night and didn't seem concerned that it was anything more than that.
It was later reopened in May 2019 after Ecuador rescinded its grant of asylum in the previous month, which allowed British police to arrest him.
He stayed there for almost seven years.
He is now serving a 50-week prison sentence in the United Kingdom for a bail violation after seeking asylum in the Ecuadorian embassy in 2012.
Mr Assange is now fighting extradition to the U.S., which accuses him of publishing secret documents. The full hearing to decide his extradition is still set for a five-day period in late February, with brief interim hearings in November and December.
Wikileaks founder Julian Assange battles extradition to U.S.to face charges for violating the Espionage Act; Greg Palkot reports from London.