Assange decided to take refuge in Ecuador's U.K. embassy -- located in London's Belgravia district, close to Hyde Park -- in June after the U.K. Supreme Court denied his extradition appeal, allowing for him to be sent to Sweden to be questioned by the police.
The U.K. Foreign Office issued a statement saying that it was disappointed that Ecuador had offered political asylum to Assange.
Under British law, with Assange having exhausted all options of appeal, authorities are under a binding obligation to extradite him to Sweden, according to the statement. It will carry out that obligation, and the Ecuadorian government's decision on Thursday does not change that, the statement said.
The U.K. Foreign Office also added that it remains "committed to a negotiated solution that allows us to carry out our obligations under the Extradition Act."
The chance is nonexistent that the country will allow Assange to leave the embassy and travel to Ecuador.
"We will not allow Mr. Assange safe passage out of the U.K., nor is there any legal basis for us to do so," Foreign Secretary William Hague said at a press conference late Thursday local U.K. time.
The secretary added: "It is important to understand that this is not about Mr. Assange's activities at Wikileaks or the attitude of the United States of America. He is wanted in Sweden to answer allegations of serious sexual offenses."
The British government has reportedly said that it will not permit Assange to leave the country to travel to Ecuador, so that country's offer of asylum would likely restrict him to staying in its London embassy, as long as the U.K. respects that as sovereign territory under diplomatic treaties. On Wednesday, the embassy posted a statement on its website objecting to what to enter the embassy forcibly.
Outside the embassy the police and Assage's supporters -- some of whom appear to be convinced he is the victim of a conspiracy -- had once again gathered outside court building, shouting "Julian Assange, freedom fighter" and "Hands off Ecuador." They waited through a downpour before getting the decision, and once it came applause and cheers erupted.
Assange's stay in the U.K. has taken many twists and turns. The Swedish Prosecution Authority issued a European Arrest Warrant for Assange in November 2010, seeking his extradition to Sweden for questioning over allegations of sexual offenses. He was then arrested in London on Dec. 7, 2010, and placed under virtual house arrest while courts examined the extradition request, which he opposed.
Once Assange was in residence at the embassy, Ecuador offered Sweden the opportunity to question him there, but the suggestion was declined.
Assange's supporters feared that, in Sweden, he could face up to a year in solitary confinement awaiting questioning and up to four years in prison if he is charged and subsequently convicted.
They also feared that, from Sweden, he could be transferred to the U.S. to face charges under that country's Espionage Act. Rumors persist that the U.S. has empaneled a federal grand jury to determine whether charges should be brought against Assange.
Two of WikiLeaks' most widely reported leaks involved U.S. diplomatic cables ("Cablegate") and video from a U.S. helicopter gunship in Iraq (the so-called "Collateral Murder" video). A U.S. Army private, Bradley Manning, is charged with leaking the documents and is being held pending a military trial.