This decision marks the culmination of an 18-month legal proceeding in Britain, but it is surely not the last twist of Assange's legal fate.
To understand the legal basis of the ruling, The Conversation spoke to Donald R Rothwell, professor of International Law at Australian National University.
Could you provide a brief explanation of what happened in the trial?
Mr Assange was appealing against the issuing of a European arrest warrant, which would have resulted in his extradition from the United Kingdom to Sweden for questioning in relation to sexual assault charges.
Mr Assange's appeal to the UK Supreme Court revolved around a legal question as to whether or not the Swedish prosecutor, who issued the arrest warrant, was, for the purposes of English law and European law, a competent judicial authority.
By a five to two decision, the UK Supreme Court dismissed the appeal and found that the Swedish prosecutor was a competent judicial authority for those purposes.
Is there a legal precedent for questioning judicial authority in extradition proceedings?
The UK Supreme Court decision does refer to precedent on this point within the European Union and makes direct reference to a decision of the Italian Courts.
However, there was no previous decision on this point in English law, and this was the basis upon which Assange sought to mount his legal appeal to the court.
If Assange were extradited to the US from Sweden, would Britain have legal grounds to intervene?
Once Assange is extradited to Sweden, he will be subject to legal processes in that country. As Assange is not a British citizen, Britain will relinquish any legal control over him during that point in time.
If Assange is to take proceedings to the European Court of Human Rights, what would be his legal case?
There may be two possible grounds for a case to go before the European Court of Human Rights.
The first would be on the interpretation issue that the UK Supreme court was addressing, which goes to the ability of a prosecutor to issue a European arrest warrant
The second issue may well relate to whether Assange's human rights in a broader sense have been infringed as a result of this process.
What's next for Assange?
If Assange is extradited to Sweden, there are three possible outcomes.
The first is that the Swedish prosecutor, upon questioning Assange, determines that he has no case to answer.
The second is that Assange is charged, faces trial and then is acquitted of charges brought against him.
The third option would be that he faces trial and is convicted of the charges brought against him. In which case he would inevitably face some jail term in Sweden.
Donald R Rothwell does not work for, consult to, own shares in or receive funding from any company or organisation that would benefit from this article, and has no relevant affiliations.