The 54-year-old former businessman has twice been found guilty of the murder of his estranged wife, Arlene Fraser.
He was jailed for life and ordered to spend at least 17 years behind bars in May last year for organising the murder of the mother-of-two whose body has never been found.
Fraser has consistently denied involvement in the disappearance of Ms Fraser who was 33 when she vanished from her home in New Elgin, Moray, on April 28 1998.
At an appeal hearing last month, Fraser's legal team argued that he was denied a fair trial.
A comment made by a witness, referring to time Fraser spent in custody, was prejudicial and may have led jurors to do their own research on the case, defence QC John Scott said.
But judges at the Court of Criminal Appeal in Edinburgh dismissed the appeal today.
Mr Scott argued that the comment made by Sandra Stewart in the witness box last year referred to a previous conviction Fraser had for assaulting his wife to the danger of her life weeks before she disappeared.
The "Google factor" increased the risk of jurors potentially finding prejudicial material on the internet if they searched for it, he said.
Lord Justice Clerk Lord Carloway, who heard the appeal with Lady Paton and Lord Drummond Young, said the court was not persuaded that the remark pointed towards the previous conviction.
"The court does not consider that there is any realistic possibility that the short answers which were given ... in isolated moments, in the course of a lengthy trial examining in detail the circumstances of Mrs Fraser's disappearance, would have promoted any recollection of a previous conviction in the minds of the Edinburgh jurors.
"Such recollection would presuppose a remarkable, and it might be reasonably surmised, implausible power of memory retention in the minds of persons with no obvious direct connection to the case, the locality or the criminal justice system."
The appeal judges accepted it would be possible for jurors to have searched the internet for information about Fraser but said that they had been reminded not to do so.
"Jurors are adults," the court opinion said.
"In this case, there were clear and repeated directions given to the jury during the trial and again at its conclusion in the charge itself, shortly before the jury retired to consider their verdict.
"In the absence of material which would tend to demonstrate the contrary, the court must proceed on the basis that the directions were followed."
The judges did not consider that Ms Stewart's comment had increased the risk of jurors researching the case online.
Directions given by trial judge Lord Bracadale immediately after her evidence were "sufficient to meet any potential prejudice to the appellant as a result of the answers", they said.
At the time Lord Bracadale had reached a "balanced and reasonable" decision about whether the comment had compromised the prospect of a fair trial and the appeal court could not fault his decision.
"The court does not consider therefore that the fairness of the trial was, or might have been perceived to be, prejudiced in any material manner," the opinion said.
"Having considered all the material it is unable to hold that it has been demonstrated that a miscarriage of justice has occurred.
"For all of these reasons, the appeal is refused."
Fraser was jailed for life and ordered to spend at least 17 years behind bars in May last year for organising the murder of mother-of-two Ms Fraser whose body has never been found.
The ex-fruit and vegetable wholesaler's conviction at the High Court in Edinburgh followed a retrial which lasted five weeks.
The trial heard that Fraser told a former friend that he paid a hitman £15,000 to kill his wife after she began divorce proceedings.
Fraser was found guilty of murder in 2003 but his conviction was quashed in 2011. A fresh trial was granted after the highest court in the land, the Supreme Court in London, ruled that the initial conviction was unsafe.
Fraser has consistently denied involvement in the disappearance of his wife who was 33 when she vanished from her home in New Elgin, Moray, on April 28, 1998.
Mrs Fraser's family, who were in court, spoke of their relief following the hearing.
Her mother Isabelle Thompson said she had been more nervous than when she waited to give evidence at the trial of her daughter's killer.
She said she was "over the moon" with the decision.
"I don't know what to feel. It will take a wee while to sink in that that's it finally finished.
"According to what we've been told, it is the end of the road now. That's the end.
"Hopefully we can get on with our lives properly instead of just day by day."
She criticised a system that had led to 15 years of uncertainty for the family.
"I always feel everything should be dealt with at the trial," she said.
"They speak about human rights and things like that, when you have committed a crime I don't think you should have any human rights. You are a criminal.
"There seem to be more criminals walking the streets through a technicality rather than that they are innocent.
"If he (Fraser) had walked free today, it wouldn't have been because he was innocent - it would be a technicality in the trial."
When asked if she had a message for First Minister Alex Salmond on the issue, she said: "Get rid of all these appeals."
Mrs Fraser's father Hector McInnes said: "I'm quite happy that it's all finished. It's a relief to know that we won't have to come back here again."
Asked if he had a message for Fraser, he said: "Not really. He committed a crime and he should do his time."
Mr McInnes said the family had been told Fraser could apply to the Scottish Criminal Cases Review Commission but had been advised it was unlikely.