Assange, who has always denied wrongdoing, has been holed up at the Ecuadorian Embassy in London since 2012, in an effort to avoid a Swedish arrest warrant.
Assange contends the United States should recognize his First Amendment rights as a journalist. Long added: "This has gone on long enough".
Samuelsson also said that the decision meant Assange "is free to leave the embassy whenever he wants", though he later told the TT news agency that he did not know when Assange might leave.
Ny told reporters that prosecutors had been unable to make a full assessment of the case and were not making a finding on whether Assange was guilty or innocent of the allegations.
After the announcement, Assange spoke with the press from the embassy's balcony: "WikiLeaks will continue to its publications".
"This implies that we can now demonstrate that the USA has a will to take action. this is why we ask for the arrest warrant to be cancelled so that Julian Assange can fly to Ecuador and enjoy his political asylum", he told AFP at the time.
"Westminster Magistrates' Court issued a warrant for the arrest of Julian Assange following him failing to surrender to the court on June 29, 2012", the force said in a statement.
Melinda Taylor, a member of Assange's legal team, called attention to the US, telling NBC News that "as long as the national security prosecution continues there continues to be a risk to him".
Swedish prosecutors received a translation of the interrogation four months later, but "all materials were translated into Spanish then into English then back into Spanish then into Swedish", Ny said, making it hard for the investigation to move forward.
The country's director of public prosecutions, Marianne Ny, said the preliminary rape and sexual assault probe has been discontinued.
Assange is wanted by British police for extradition to Sweden.
He has been in the Ecuadorian embassy in London since June 2012, claiming political asylum in order to escape a European Arrest Warrant over the claim.
But it adds that Assange is now wanted for a "much less serious offence" than the original sex crimes claims, and police "will provide a level of resourcing which is proportionate to that offence".
A Swedish court upholds the European arrest warrant against Assange.
Ms Ny said the motive for her decision was that there is no reason to believe the decision to surrender Mr Assange to Sweden can be executed in the foreseeable future.
"This implies that we can now demonstrate that the U.S. has a will to take action. this is why we ask for the arrest warrant to be cancelled so that Julian Assange can fly to Ecuador and enjoy his political asylum", lawyer Per Samuelsson told AFP at the time.
As NPR's Frank Langfitt reports, Assange has remained at the Ecuadorean Embassy for years out of fear that an extradition to Sweden would spell another extradition, in turn, to the USA, "where he could face trial for leaking hundreds of thousands of secret diplomatic and military documents".
"UK refuses to confirm or deny whether it has already received a U.S. extradition warrant for Julian Assange".
Kim Dotcom, the founder of now-defunct file hosting service Megaupload, also responded to the news of the rape investigation against Assange being dropped in Sweden. "Focus now moves to United Kingdom", the group tweeted.
August 13: Swedish prosecutors drop investigations into some allegations against Assange because of the statute of limitations; investigation into a rape allegation remains active.
Police kept up round-the-clock guard outside the embassy until past year, when the operation was scaled back.
There were initially two separate allegations being investigated, but one was dropped in 2015 because the statute of limitations ran out.