"It is now the task of the states of Sweden and the United Kingdom as a whole to implement the verdict," the WikiLeaks founder said through a video link from the embassy shown at a press conference in London.
"We have a really significant victory that has brought a smile to my face," said the lanky 44-year-old Australian hacker, who has published millions of classified military and diplomatic documents for years.
"It is the end of the road for the legal arguments... Those arguments lost. There is no appeal. The time for appeal is over," said Assange, who looked pale and dishevelled and spoke in a monotone.
"I've been detained without charge in this country, the United Kingdom, for five and a half years... I've had great difficulty seeing my family and my children," he said.
British Foreign Secretary Philip Hammond earlier dismissed the UN panel opinion as "ridiculous".
Assange reacted to that saying: "I find those comments to be beneath the stature that a foreign minister should express."he added "This is a serious finding,".
Police have said they are obliged to detain Assange if he sets foot outside the embassy on British soil because of a European arrest warrant against him stemming from a rape allegation in Sweden.
He has exhausted all appeals in British courts against an extradition to Sweden.