The Lord Justice Clerk, Lord Carloway, sitting with Lady Dorrian and Lord Bracadale, has granted the Crown authority to bring a new prosecution against 68-year-old Angus Sinclair.
They granted an application under the Double Jeopardy (Scotland) Act 2011 and set aside his earlier acquittal, paving the way for a new trial.
The bodies of 17-year-olds Christine Eadie and Helen Scott were found in East Lothian in October 1977 after they had earlier been seen at the World's End pub in Edinburgh's Royal Mile.
Mr Sinclair previously stood trial at the High Court in Edinburgh charged with their murders in 2007 but the judge, Lord Clarke, brought proceedings to an end by ruling there was no case to answer.
It would be the first retrial to be held after the double jeopardy legislation was amended in November 2011.
Before the new laws came into force, people could not be retried for the same crime.
Following the passing of the new legislation by the Holyrood Parliament the Crown asked the Court of Criminal Appeal in Edinburgh for the acquittal to be set aside and also sought authority for a fresh prosecution.
The original murder investigation was one of the largest to ever take place in Scotland, with police collating a list of more than 500 suspects and taking more than 13,000 statements from members of the public.
An image of the two young women, which was taken in a photobooth, became a well-known image from the murder case.
However, the investigation was closed in May 1978 with no arrests being made.
The inquiry was eventually reopened 1997 by the former Lothian and Borders force's cold case unit.
A later BBC Crimewatch appeal, in 2003, attracted 130 calls from new witnesses.