Mr Assange took refuge there three years ago to avoid extradition to Sweden on charges of sexual assault against two women in 2010.
He denies the accusations and says he fears Sweden would extradite him to the United States for possible trial there.
In 2010 Wikileaks published a huge number of US classified documents.
Britain has accused Ecuador of perverting the course of justice by allowing Mr Assange to remain in its embassy.
A spokeswoman for the Foreign Office said, "It is for the Swedish prosecutor to decide how they now proceed with the legal case."
The agreement was signed in Ecuador after about six months of investigations.
The co-ordinator of Mr Assange's international legal defence team, Baltasar Garzon said, "Julian Assange's rights need to be respected by Sweden and the United Kingdom. These countries have failed to do so until now.
"Julian Assange's only demands are that his fundamental rights are acknowledged and respected, including the asylum granted to him by Ecuador."
According to the British news agency PA, it is unlikely Mr Assange will be questioned by Sweden until the New Year.
Anti-secrecy group WikiLeaks said on Monday that its founder Julian Assange's internet was shut down by the government of Ecuador, deflecting blame from the U.S. or British governments which have sparred with Assange for releasing sensitive material.
5 years, 11 months ago
The UK government may have stopped its 24/7 surveillance of the Ecuadorian embassy where Julian Assange is seeking refuge, but it is still determined to arrest him the moment he sets foot outside.
6 years, 11 months ago