Appeal judges concluded that there was "overwhelming evidence" Colin Coats and Philip Wade were guilty of killing Lynda Spence.
Coats, 43, was sentenced to a minimum of 33 years in April last year after a judge concluded he was the "prime mover" in the abduction, torture and killing of the 27-year-old, whose body has never been found.
Wade, also 43, was ordered to spend at least 30 years behind bars after being convicted of the same charge at the High Court in Glasgow.
Both men launched appeals claiming that they were the victims of a miscarriage of justice. Their legal teams said trial judge Lord Pentland was wrong to dismiss an objection to a line of evidence during the trial. The evidence involved a statement made by Wade that he had recently killed someone and needed to find a way to dispose of the body.
But the appeal judges - Lord Justice General, Lord Gill, sitting with Lord Menzies and Lord Turnbull - agreed that trial judge Lord Pentland had been entitled to refuse the objection.
Lawyers for Wade and Coats also argued that the Crown had not properly disclosed the fact that Ms Spence had been recruited as a covert intelligence source by the Scottish Crime and Drug Enforcement Agency a month before she disappeared in April 2011.
This had prejudiced the defence and led to a miscarriage of justice, they told a hearing at the Court of Criminal Appeal in Edinburgh.
But Lord Gill said: "There emerged, in my view, an overwhelming case that the appellants murdered the deceased. In my opinion, there was no miscarriage of justice."
On the sentencing appeal, he added: "This was a barbaric crime that merited the severest penalty."
Jurors heard how Ms Spence was abducted from Broomhill Path, Glasgow, on April 14, 2011 and driven to a flat in West Kilbride, after she tried to involve Coates in a corrupt land deal centred on Stansted Airport.