He said: "How sweet it is this is a victory that cannot be denied. It is a victory of historical importance, not just for me, my family, my children but the independence of the UN system.
"I'm tough, I'm hardened by this process and I can take it. However, what right does this government or the US government or the Swedish government have to deny my children their father for five and a half years without any charges in any country?
"That is a fact I will never forget."
Mr Assange said Sweden and the UK had opportunities in the past few weeks to appeal against the decision but had not taken any action, so the matter was now a "settled law".
He said: "It is the end of the road for legal arguments by the UK and Sweden. Those arguments lost and the time for an appeal is over.
"It is now the task of the states of the UK and Sweden to implement the verdict. They cannot pretend to look tough."
He finished his comments by saying he missed his family, adding: "We have a really strong victory that has brought a smile to my face and I hope many others as well."
Melinda Taylor, part of Mr Assange's legal team, said the UN report made clear that the WikiLeaks founder was neither a fugitive from justice, nor could he just walk out of the embassy.
She called it a "damning indictment" of the way Mr Assange has been treated and showed his willingness to co-operate with the Swedish investigation.
But Mr Hammond said: "I reject the decision of this Working Group. It is a group made up of lay people and not lawyers.
"Julian Assange is a fugitive from justice. He is hiding from justice in the Ecuadorian embassy.
"He can come out any time he chooses ... But he will have to face justice in Sweden if he chooses to do so.
"This is, frankly, a ridiculous finding by the working group and we reject it."
