British police said they would still arrest Assange if he tried to leave the embassy.
"The European Arrest Warrant no longer holds. The UK must now grant safe passage to Mr Julian Assange," minister Guillaume Long wrote on Twitter.
Swedish prosecutors earlier announced they had dropped their rape probe against Assange, 45.
Despite that, British police said they would still arrest Assange if he tried to leave the embassy.
They said he had breached the terms of his bail by refusing to turn himself in when an arrest warrant was issued in 2012.
The Australian founder of the WikiLeaks whistleblowing site has always denied the rape allegations.
His site in 2010 leaked hundreds of thousands of secret US military and diplomatic documents.
Assange feared that if he gave himself up to the Swedish authorities he would be extradited to the United States and put on trial for the intelligence leaks.
Ecuador under leftist President Rafael Correa granted Assange asylum in its London embassy in 2012.
Long said "Ecuador welcomes the decision to drop the charges," recalling that Swedish prosecutors questioned Assange in the embassy in November.
"Ecuador regrets that it took Swedish Prosecutor more than four years to carry out this interview. This was a wholly unnecessary delay," Long wrote.