Swedish prosecutors announced the closure of the preliminary investigation on Tuesday due to weakening of evidence, Efe news reported.
Deputy Chief Prosecutor Eva-Marie Persson said in a press conference in Stockholm: "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 there is no longer any reason to continue the investigation."
Assange, who denied the accusation, avoided extradition to Sweden for seven years after being granted asylum in the Ecuadorian embassy in London in 2012.
The investigation was first opened in 2010 and closed in 2017, before being reopened earlier this year after he was removed from the embassy and arrested.
Kristinn Hrafnsson, WikiLeaks editor-in-chief, said in a statement, "Let us now focus on the threat Assange has been warning about for years: The belligerent prosecution of the United States and the threat it poses to the First Amendment?"
Assange rose to international attention nine years ago after WikiLeaks published leaked military information provided by former US Army soldier Chelsea Manning, which prompted the US government to launch a criminal investigation into the publisher.
In November that year, Sweden requested his extradition over allegations of sexual assault and rape.
Assange denied the allegations and also expressed concerns that he would be extradited from Sweden to the US because of his role in the Manning leaks.
Assange surrendered before the UK police around a month later and was held in custody for 10 days before being released on bail.
When he was unable to challenge the extradition proceedings, he breached bail and in August 2012 was granted asylum by Ecuador.
Sweden later withdrew its extradition request, but a UK arrest warrant remained in force as Assange had failed to surrender after breaking bail conditions.
He was taken into custody by the capital's Metropolitan Police in April for failing to surrender to court in the UK and on a US extradition warrant.
Assange faces charges, including computer intrusion in America.
He is currently being held at Belmarsh prison in London while his extradition to the US is being considered by UK courts.
( With inputs from IANS )