The London-based court said the conviction was unsafe, and returned Fraser's case to the court of appeal last month - giving Scottish judges the option of entirely quashing Fraser's conviction and setting him free, or ordering a fresh trial.
The supreme court's jurisdiction has been attacked by Alex Salmond, the first minister, and his justice secretary Kenny MacAskill, who claimed the supreme court was interfering with Scotland's independent legal system.
The court of appeal in Edinburgh, headed by Lord Hamilton, the lord justice general, formally set aside Fraser's original conviction on Friday afternoon and, after refusing bail and remanding him in custody, agreed to a prosecution application for a fresh trial.
Arlene Fraser's body has never been found. Fraser, 52, has consistently said he was not guilty of her murder.
Fraser appealed in 2006 but his case was thrown out by the court of appeal, who ruled his conviction was safe.
The supreme court, led by its deputy head and a former lord justice general of Scotland, Lord Hope, said Fraser's original conviction was made unsafe because the prosecution had failed to disclose significant evidence.
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Nat Fraser - Conviction for murder quashed by Supreme Court
Fraser (Appellant) v Her Majesty's Advocate (Respondent) UKSC 24
On appeal from the High Court of Justiciary HCJAC 27
Justices: Lord Hope (Deputy President), Lord Rodger, Lord Brown, Lord Kerr, Lord Dyson
Judgment
The Supreme Court unanimously allows the appeal. It remits the case to a differently constituted Appeal Court to consider whether to grant authority for a new prosecution and then, having considered that point, to quash the conviction. Lord Hope gives the main judgment, with which Lords Rodger, Kerr and Dyson agree. Lord Brown gives a separate judgment indicating his reservations about allowing the appeal, but does not dissent.