He has been holed up in the Ecuadorian embassy in London for the past two months.
The decision was announced on Thursday in Quito by the Ecuadorian Minister of Foreign Affairs, Ricardo Patiño.
Patiño said the country wanted to uphold its tradition of protecting those who were vulnerable, and thus believed Assange's fears of political persectuion to be "legitimate".
Speaking to staff at the embassy in London, Assange said "it is a significant victory for myself, and my people. Things will probably get more stressful now".
Although the British Foreign Office found this news to be disappointing, it issued a statement saying "under our law, with Mr. Assange having exhausted all options of appeal, the British authorities are under a binding obligation to extradite him to Sweden."
It said it remains committed to reaching a "negotiated solution" that will allow it to respect its obligations under the Extradition Act.
In other words, Assange can still be arrested once he steps outside the Ecuadorian embassy.
Furthermore, Ecuadorian officials said they received a written warning from Britain saying that British police could enter the Ecuadorian embassy to arrest Assange under the Diplomatic and Consular Premises Act of 1987 that grants the UK the right to revoke the diplomatic status of a building.
Assange sought refuge in the embassy on 19 June after he had exhausted all other options for appeals to remain in the UK and avoid extradition to Sweden, where charges of sexual offences await him.
In 2010, two former female Wikileaks volunteers accused him of committing such offences while he was in Stockholm giving a lecture.
The founder of Wikileaks, a website of leaked diplomatic cables that caused embarassment to many governments, particularly the US in 2010 over its operations in Iraq, is especially fearful that if he goes to Sweden, he will eventually be handed over to American authorities.