The Scottish government is set to introduce legislation that could see Angus Sinclair stand trial over the World's End murders for a second time.
The proposals to end the double jeopardy rule were disclosed by Justice Secretary Kenny MacAskill in an exclusive interview with BBC Scotland.
Sinclair was cleared in 2007 of killing Helen Scott and Christine Eadie.
Mr MacAskill said the Crown would have the government's "full support" if it wished to re-prosecute Sinclair.
Sinclair's trial for killing Ms Scott and Ms Eadie, in what became known as the World's End murders, controversially collapsed after a High Court judge ruled he had no case to answer - although police and relatives of Ms Scott and Ms Eadie remain convinced of his guilt.
The laws on double jeopardy prevent anyone who has already been cleared of committing a crime from standing trial for a second time over the same offence, even if new evidence comes to light.
But signalling his intention to end the 800-year-old rule, Mr MacAskill said if fresh evidence against Sinclair was found in the World's End case, the hands of prosecutors should not be tied.
He said: "People who commit heinous crimes and for whatever reason closure does not occur, we owe it to the victims, to the families, to the communities to allow action to be taken.
"The decision about whether a case should be re-prosecuted and double jeopardy should be overturned will ultimately be a matter for law officers.
"But our view is that the law officers should have the right, and if it is retrospective, then so be it. The law officers will have our full support."
Mr MacAskill, who said the World's End case had "scarred the soul of Scotland", stressed that exceptions to the double jeopardy rule should only occur when new and compelling evidence emerged, or an admission of guilt was made.
But he said the government had "a direction of travel" that had to reflect the 21st Century.
The move would bring Scotland into line with changes made to the law in England and Wales four years ago, since when there have been three successful re-prosecutions.
However, it would go against recommendations made last week by the Scottish Law Commission, which said any change to the law should not be applied to cases retrospectively.
It is likely the matter will come before the Scottish Parliament early next year, and with opposition parties signalling their support for a change to the double jeopardy law it is likely to pass through easily.
BBC Scotland understands the Crown has carefully preserved forensic evidence from Sinclair's trial, and is re-examining all aspects of the case - particularly the DNA - with a view to launching a fresh prosecution against him.
Sinclair, who has a long history of sexual violence and is currently serving a life sentence for the murder of Mary Gallacher in 1978, is suspected of being a serial killer who is also responsible for the deaths of at least six other women, including Ms Scott and Ms Eadie.
The bodies of Ms Scott and Ms Eadie, who were both 17, were found about six miles apart in East Lothian in 1977.
The teenage friends, who were last seen alive leaving the World's End pub in Edinburgh's Royal Mile, had both been stripped, beaten and sexually assaulted. Sinclair's DNA was found at the scene.
Morain Scott, the father of Helen Scott, welcomed the potential abolition of double jeopardy.
He told the BBC: "Our understanding is that all political parties are in support of changes to the double jeopardy rule and we hope that early agreement will be reached and our Scottish Parliament will make the right decision and allow the re-trial of Angus Sinclair for the murders of Helen and Christine.
"The comments made by Kenny MacAskill give us some confidence that we will still get the closure that we expected two years ago and we look forward to justice being delivered this time."
Paul McBride QC, who spoke out strongly against the Law Commission's decision last week, also welcomed the announcement.
He said: "I'm delighted that the justice minister has decided to overturn the patently illogical recommendation from the Scottish Law Commission and follow the path preferred by all the other political parties as well as the public.
"If one thinks of rape cases involving children, rape cases involving adults, horrific murder cases, and new evidence of a compelling nature comes to light that wasn't available at the trial that demonstrates beyond any question the person is guilty, is it right as a society to say that persons should go free?"
Scotland's Secret Serial Killer will be broadcast on Thursday at 2100 GMT on BBC2 Scotland and will be available on the BBC iPlayer.