Assange took refuge there to avoid extradition to Sweden, where he faces sexual assault allegations. British authorities still vow to arrest him if he leaves the embassy.
"We're at something of an impasse," lawyer Rebecca Niblock said shortly after the news broke. "It's not a question of law anymore. It's a question of politics and diplomacy."
Assange made national headlines after his website repeatedly released scores of secret U.S. documents.
The 41-year-old, who denies the sexual assault accusations, has expressed fears that the case is the opening gambit in a Washington-orchestrated bid to make him stand trial for his leaks in the United States - something disputed by both by Swedish authorities and the women involved.
In a mark of its anger over Ecuador's ruling, the Swedish Foreign Ministry said it had summoned Ecuador's ambassador over the decision.
"We want to tell them that it's unacceptable that Ecuador is trying to stop the Swedish judicial process," spokeswoman Anders Jorle said.
British authorities also said in a statement that it was disappointed by the decision to offer Assange asylum - noting that he had exhausted every appeal possible over the course of a roughly 18-month-long legal saga.
The Associated Press contributed to this report.
