Assange meanwhile guest-starred as himself in an episode of "The Simpsons", recording his lines over the phone from the Ecuadoran embassy.
Marianne Ny, Sweden's director of public prosecution, said in a statement that the rape investigation was dropped because "there is no reason to believe that the decision to surrender him to Sweden can be executed in the foreseeable future".
"My assessment is the transfer can not be carried out in a foreseeable future", Ny told a news conference in Stockholm, adding that Assange had avoided all attempts by British and Swedish authorities to arrest him.
Assange, 45, took refuge in the embassy in June 2012 to avoid extradition to Sweden over the rape allegation, which he denies. More serious are the possible charges he faces in the United States for WikiLeaks' aggressive publication of thousands of pages of classified government documents.
In a statement, chief Swedish prosecutor Marianne Ny said she had chose to "discontinue" the investigation into Assange over a rape allegation dating back to 2010 as there were no further avenues to pursue to take the probe forward. "Therefore the investigation is discontinued".
The divisive founder of WikiLeaks has repeatedly denied the accusations of rape and molestation made by two women he met during a trip to Stockholm in 2010.
March: Swedish prosecutors ask to question Assange at the Ecuadorean embassy.
However, London police issued a statement after the Swedish announcement making clear Assange was still wanted by them.
Updated at 11.46 UTC to add: Swedish prosecutors apparently chose to drop the charges because there is "no reason to believe" he will be surrendered to the country's authorities in the foreseeable future.
Previously, Assange promised to leave the embassy if Chelsea Manning was granted clemency.
Spalletti: "C'è solo il Chievo". Il futuro e Totti sono tabù
Noi dobbiamo essere bravi a modificare le nostre capacità per poter togliere loro tutte queste caratteristiche. La società prendendo Monchi fa vedere che vuole portare i migliori a lavorare nella Roma .
On November 20, Interpol issued a Red Notice for Mr Assange's arrest.
A Swedish court upholds the European arrest warrant against Assange. We have won the Assange case.
Another lawyer, Christophe Marchand, told AFP that "We have been waiting a long time for this decision". He did not take shouted questions from the reporters assembled outside and would not say if he plans to leave the embassy located in the posh Knightsbridge neighborhood.
September 27: Assange leaves Sweden for Britain.
October 24 - Assange says WikiLeaks will have to stop publishing secret cables and devote itself to fund-raising. The U.N. Working Group on Arbitrary Detention ruled that Assange had been "arbitrarily detained by the Governments of Sweden and the United Kingdom of Great Britain and Northern Ireland".
"Westminster Magistrates' Court issued a warrant for the arrest of Julian Assange following him failing to surrender to the court on the 29 June 2012", British police said.
Today, they said Assange was previously wanted for "an extremely serious offence" in Sweden and the police presence around the embassy had "reflected the serious nature of that crime". Last month, the United States attorney general, Jeff Sessions, said the arrest of Assange was a "priority" after the CIA director, Mike Pompeo, described WikiLeaks as a "hostile intelligence service" and a threat to U.S. national security.
British police kept up a round-the-clock guard outside the embassy until December 2015, when the operation was scaled back partly because of the costs, which had exceeded 11 million pounds (over $17.5 million at the time).
In a tweet, Wikileaks said the "focus now moves to the UK".