Following unprecedented criticism of the UK's most senior judges, ministers called for a new system to give Scottish judges the power to agree or veto which cases could be referred to the London-based court.
However, following opposition from the Advocate General and others, ministers have been forced to drop the plan for such "certification".
In a significant indication of who determines such matters, the UK Government has rejected the proposal.
Instead, a review group will be set up, led by the Lord President, Scotland's most senior judge, to report back in three years.
Last year, following the Supreme Court decision to over-turn a Scottish murder conviction, the First Minister and Justice Secretary Kenny MacAskill personally criticised the judges.
They accused the Supreme Court of "intervening aggressively" in Scottish cases, of "opening cell doors" and of being ignorant about the law. Mr MacAskill also threatened to cut funding to the court.
Many senior lawyers and judges were stunned as the comments appeared to attack the professionalism of Scotland's two supreme court judges, Lord Hope and Lord Rodger.
Following the row, ministers commissioned retired Scottish judge Lord McCluskey to review the Supreme Court's role.
Mr McCluskey's panel supported the Supreme Court's role in adjudicating on European human rights convention breaches in criminal trials, but said the decision on which cases could be referred to London should lie with Scottish judges. Mr MacAskill was quick to back this recommendation.
In the autumn the Sunday Herald revealed Lord Hope had hit back, quoting remarks made to him by the late Lord Rodger on the "corrosive anti-English sentiment" in Scotland's courts, and describing it as an obstacle to legal progress.
Lord Hope warned against moves to limit the court's ability to hear appeals against Scottish convictions.
The UK Government has not agreed to certification but agreed on a review. Lord McCluskey has lodged amendments and the House of Lords is considering various amendments.
A Scottish Government spokesman said: "Agreement has been reached between governments that creates a distinct and coherent system for the UK Supreme Court to deal with human rights issues in Scots criminal law.
"The Scotland Bill contains a provision that the new system will be reviewed after three years, with the Lord President heading a review panel.
"The review will consider whether the High Court should have a certification power. That power would allow the High Court of Justiciary rather than the UK Supreme Court to have the final say on whether a human rights issue raised in a Scottish criminal case is of sufficient general interest to be referred to the UK Supreme Court.
"This is used in the other jurisdictions of the UK for human rights issues in criminal cases."
The row began after the Cadder decision, which said the Scottish legal process would have to change to comply with European human rights legislation. The change meant suspects would be allowed access to a lawyer when questioned by the police.
Lord Hope said the Cadder case had been a "catalyst" for change and that Lord McCluskey's approach had not been "tactful".
He said Lord Rodger would not have been in favour of calls for certification by Scottish courts.
In contrast, Lord Hamilton, Scotland's most senior judge, publicly supported certification.