The Crown Office has applied to the High Court to set aside the acquittals of Ronnie Coulter, Andrew Coulter and David Montgomery, and prosecute them again over the death of Surjit Singh Chhokar.
Mr Chhokar, 32, was killed in Overtown, North Lanarkshire, on November 4 1998.
The murder sparked controversy after the failure of authorities to secure a conviction for the killing despite the arrests of three men and two subsequent trials.
A statement from the Crown Office said: "The Lord Advocate, Frank Mulholland QC, has today applied to the High Court for authority under the Double Jeopardy (Scotland) Act 2011 to set aside the acquittal of Ronnie Coulter, Andrew Coulter and David Montgomery, and prosecute them again for the murder of Surjit Singh Chhokar."
It is the second application to be made under the legislation since the reform of Scotland's centuries-old double jeopardy law in 2011.
Two official inquiries were ordered in the wake of the original trials over Mr Chhokar's death. One made allegations of "institutional racism".
Following the publication of the reports in 2001, the then Lord Advocate, Colin Boyd QC, said the Chhokar family had been failed by the police and prosecution services.
In January 2012, police said they had been instructed by the Crown Office to carry out a new investigation into the unsolved murder of Mr Chhokar.
Mr Chhokar's family met prosecutors before they instructed police to reinvestigate the case two years ago and today the Lord Advocate told them about the application for a new trial.
Solicitor Aamer Anwar said the family "will only ever be at peace when there is justice".
"Today the family were advised by the Lord Advocate that the Crown will make an application to the appeal court under double jeopardy legislation to bring fresh proceedings for murder against three men," Mr Anwar said.
"There still remains significant legal hurdles to be overcome.
"The Chhokar family are grateful to the Crown Office and Police Scotland for their determination and support.
"Today is an important step but the Chhokar family will only ever be at peace when there is justice."