Lord Gill said: "The circumstantial evidence alone constituted a compelling case against the appellant."
Fraser was led away, carrying a notebook, to begin the remainder of his sentence.
Grampian Police Assistant Chief Constable Jim Stephen said: "Today's result means that Nat Fraser will continue to pay for his crime. This must be a source of comfort to Arlene's family who have had to endure considerable pain and anxiety throughout the appeal period.
"Their support for Grampian Police has been unstinting and their patience and strength have been quite remarkable. We hope that in some way today's verdict will help them close one traumatic chapter of their lives.
"This outcome recognises the hard work and commitment of the Arlene Fraser inquiry team, which demonstrated, throughout, a commendable level of determination and professionalism in the face of a difficult and complex investigation."
Hunt for truth
Scotland's Solicitor General, Frank Mulholland QC, said: "I am pleased that the Appeal Court has today upheld Nat Fraser's conviction for the murder of his wife Arlene.
"This was an appalling crime and the decision of the Appeal Court will be a small comfort to Arlene's family that justice has been done. Our thoughts remain with Arlene's family at this time."
The appeal decision came just a few days after the 10th anniversary of Arlene's disappearance.
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