Fatjon Kapri fled to Glasgow after allegedly stabbing a man to death in London in 2001 and worked in the Blue Lagoon chip shop on Gordon Street in the city centre.
He took a false Macedonian identity, Sadiku Saymire, and began a relationship with a co-worker.
But he had been convicted in his absence in Elbasan, Albania, in 2002 for murdering the man, another Albanian national named Ylli Pepa, and given a 22-year jail term.
The Albanians asked the British authorities to send Kapri back but the 30-year-old escaped from the Metropolitan Police.
In 2010, he was traced to Glasgow and arrested by Strathclyde Police officers. After a lengthy appeal process, during which Kapri claimed the Albanian court system was corrupt, three judges at the Court of Criminal Appeal in Edinburgh refused his request not to be extradited.
But now a five-judge panel at the Supreme Court in London, headed by Lord Hope, has ruled that sending Kapri back to Albania would breach his right to a fair trial under Article Six of the European Convention on Human Rights.
Albania joined the Council of Europe in 1995 and ratified the ECHR in 1996.
Today's Supreme Court ruling said: "The new argument (by Kapri's legal team)…was supported by averments…that the judicial system in Albania was systemically corrupt. They incorporated a number of reports...by, among others, the European Commission, the Swedish International Cooperation Agency and the US Department of State, Bureau of Democracy, Human Rights and Labour."
The judges, Lord Hope, deputy president of the Supreme Court, Lady Hale, Lord Kerr, Lord Sumption, and Lord Toulson concluded: "It is a sad fact that, despite all the many provisions in international human rights instruments which emphasise that everyone has the right to a fair trial before an independent and impartial judge, there are still states where the judiciary as a whole is infected by corruption.
"It is, of course, hard to get at the true facts. But there is no smoke without fire, and where allegations of corruption are widespread they must be taken seriously. So too must an appreciation of what corruption may lead to when it affects the whole system. It may involve simple bribery of judges and court officials, or it may involve interference with the judicial system for political reasons of a much more insidious kind. Unjust convictions may result, just to keep the system going and keep prices up.
"Everyone whose case comes before the courts of that country where practices of that kind are widespread is at risk of suffering an injustice. Those who are familiar with the system may know how much they need to pay, or what they have to do, to obtain a favourable decision but be quite unable to come up with what is needed to achieve that. Those who are not familiar with it will be at an even greater disadvantage.
"The proper course, therefore, is for the case to be returned to the Appeal Court (in Edinburgh) so that it can be provided with up-to-date information and reach a properly informed decision as to whether or not the threshold test (on corruption in the Albanian system) is satisfied.
"The further delay that will result in the resolution of these proceedings is regrettable. But it is of the highest importance that due process be observed in matters of this kind.
"It is always tempting to resort to short cuts. But where a person's liberty and his right to a fair trial is at issue that temptation must be resisted. It is plain that the matter must be properly investigated before a decision is taken as to whether the appellant's extradition to Albania should go ahead."
They say there is new evidence about Albania available to Lord Advocate Frank Mulholland which can be debated at a new hearing.
Kapri will remain in custody meantime.