The Australian national has previously expressed concern that he could end up being extradited and facing the death penalty in the United States over allegations of revealing government secrets through his site, WikiLeaks.
On Friday afternoon, Assange appeared on a balcony at the embassy and described the development as "an important victory."
"But it by no means erases seven years of detention without charge under house arrest and almost five years here in this embassy without sunlight," Assange said. "Seven years without charge while my children grow up without me. That is not something I can forgive. It is not something I can forget."
Despite Friday's announcement by Swedish prosecutors, Assange, who is still the subject of a UK arrest warrant, acknowledged he is unlikely to walk out of the embassy any time soon.
"The proper war is just commencing," he told the crowd of reporters and onlookers gathered outside the embassy. "The UK has said it will arrest me regardless. The US CIA Director (Mike) Pompeo and the US attorney general have said that I and other WikiLeaks staff have no ... First Amendment rights, that my arrest and the arrest (of) my other staff is a priority. That is not acceptable."
Assange added that WikiLeaks would continue regardless of "the threats towards me and my staff" before hailing the release of Chelsea Manning, the former Army intelligence analyst who provided classified information to WikiLeaks
Before his balcony appearance on Friday, Assange, now 45, took to Twitter to share an an old image of himself smiling.
A lawyer for one of the Swedish women who accused Assange of sexual assault said the prosecution decision to drop the investigation was a "scandal."
Is he facing US charges?
Authorities in the United States have prepared charges to seek his arrest
, US officials familiar with the matter told CNN last month.
The Justice Department investigation of Assange and WikiLeaks dates to at least 2010, when the site first gained wide attention for posting thousands of files stolen by Manning.
Britain and the US have an extradition treaty, so if Assange leaves the Ecuadorian Embassy where he's claimed asylum, the British could arrest him and send him to the US.
Barry Pollack, an attorney in Washington representing Assange, said the British should allow Assange to travel to Ecuador.
"The decision by the Swedish prosecutor only highlights the fact Mr. Assange has been unlawfully detained for years," Pollack said. "At this point, it is more apparent than ever that the UK should provide Mr. Assange safe passage to Ecuador. Ecuador has granted Mr. Assange asylum. Recent comments by the United States attorney general and director of the CIA demonstrate the obvious need of Mr. Assange for asylum. The UK no longer has any legitimate basis to interfere with Ecuador's lawful decision."
The UK government declined to comment Friday on whether the US has asked for Assange's extradition, but last month US Attorney General Jeff Sessions said Assange's arrest was a "priority."
What did Sweden say?
Sweden's chief prosecutor Marianne Ny told a news conference in Sweden that the decision to discontinue the preliminary investigation into the rape allegations, which date back to 2010, had been made because "all possibilities to advance the investigation have now been exhausted."
However, if Assange were to return to Sweden before the statute of limitations for the suspected offenses expires in August 2020, the investigation could be reopened, she said.
Dropping the investigation is not a result of deciding he is not guilty, Ny added -- it's because there's no practical way to continue it.
"The decision to discontinue the preliminary investigation is not because we've been able to make a full assessment of the evidence in this case, but because we didn't see any possibilities to advance the investigation forward. So we don't make any statements on the issue of guilt," she said via a translator.
Lawyer: Accuser 'shocked'
Elizabeth Massi Fritz, the lawyer for Assange's accuser, criticized the Swedish authorities' decision in a statement to CNN.
"It is a scandal that a suspected rapist is able to evade the judicial system and thus avoid trial," Fritz said. "Evidence in the case is available and that evidence should have been tested in court."
Fritz said the process had dragged on for too long and that her client was "shocked" by the decision to drop it now. "To conduct a preliminary investigation for so many years and today make a decision to close the investigation is something I am very critical of," she said.
Fritz also called for a review of parts of the judicial process, including how Sweden tries suspects who deliberately avoid court for years.
"He has acted like this consciously and his fear must be that he is afraid of being sentenced for rape. Nobody wants to be sentenced for rape because it's a terrible and humiliating crime," she concluded.
CNN is not naming the alleged victim whom Fritz represents.
What's next for Assange?
Possible US charges aside, Assange is still subject to an arrest warrant in the UK after he failed to surrender to Westminster Magistrates' Court in June 2012, London's Metropolitan Police Service said Friday.
However, it noted that now that the Swedish authorities had dropped their investigation, Assange was "wanted for a much less serious offence" than before and said the force would "provide a level of resourcing which is proportionate to that offence."
It added: "The priority for the MPS must continue to be arresting those who are currently wanted in the Capital in connection with serious violent or sexual offences for the protection of Londoners."