The 45-year-old has been living in the Ecuadoran embassy in London since 2012, after seeking asylum.
"We have been waiting a long time for this decision," Christophe Marchand, a member of Assange's Brussels-based legal team, told AFP.
"Julian Assange has been a victim of a huge abuse of procedure. We are very pleased and very moved, as this marks the end of his nightmare."
He said that lawyers for the Australian, who are based around the world, were discussing the implications of the decision.
Assange posted a picture on Twitter of himself smiling broadly, without comment.
The 45-year-old has been living in the Ecuadoran embassy in London since 2012, after seeking asylum to avoid extradition to Sweden to face allegations of rape dating back to 2010.
He has always denied the claims, which he feared would see him extradited to the United States and tried over the leaking of hundreds of thousands of secret US military and diplomatic documents.