Fruit and veg salesman Nat Fraser, 54, has been found guilty twice of arranging the hit-man murder in 1998.
Fraser went to the Court of Criminal Appeal in Edinburgh to claim that the "Google factor" had made his trial last year unfair.
A chance remark by a witness may have led jurors to material that revealed Fraser had already served time for a vicious attack on Arlene in their Elgin home.
When Arlene, 33, disappeared from the Smith Street address in April 1998 Fraser was awaiting trial on a charge of attempted murder.
Defence QC John Scott told the appeal judges: "The Google factor is now well recognised in this and other jurisdictions."
But Lord Justice Clerk Lord Carloway, sitting with Lady Paton and Lord Drummond Young, rejected any suggestion Fraser had suffered a miscarriage of justice.
Outside court, Arlene's mother, Isabelle Thompson, said: "We are over the moon."
Her father Hector McInnes, 72, said he intended to celebrate. "It is a relief to know we will not be back here again."
Although yesterday's ruling at the Court of Criminal Appeal should be final, Fraser could ask the Scottish Criminal Cases Review Commission - which investigates possible miscarriages of justice - to back his fight to clear his name.
There may also be an avenue of appeal to Europe.
Mr Scott would only say that Fraser's legal team were studying the appeal judges' decision and no further move had been decided.
A hearing last month was told the trial last May should have been halted when cafe owner Sandra Stewart let slip that Fraser had recently been in prison.
Mr Scott argued that might have prompted jurors to ignore warnings from trial judge Lord Bracadale and do some "research".
They could have discovered that Fraser had spent a few days on remand after being charged with attempting to murder Arlene - an attack which was described as "the last straw" in their marriage and for which Fraser later served a jail sentence after pleading guilty to a reduced charge.
Trial judge Lord Bracadale ordered jurors to ignore the "irrelevant and inappropriate remark".
Lord Carloway said there were "clear and repeated directions" from Lord Bracadale.
Lord Bracadale was right not to halt the trial after Mrs Stewart's remark. "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."
At the end of Fraser's second trial in May last year Lord Bracadale ordered him to serve at least 17 years before he could apply for release on licence.
Two trials have heard Fraser hired a hit-man to murder Arlene.
After the first guilty verdict in 2003, Fraser lost one appeal then went over the heads of Scottish judges to the Supreme Court.
Years of legal wrangling led to a re-trial because information about the disappearance and re-appearance of Arlene's rings had not been passed on to defence lawyers.
After a second guilty verdict in May last year Fraser began the appeal process again.
Both trials have rejected Fraser's alibi - that he was on his delivery rounds - and his claim that another man was the killer.
Both juries heard that Fraser was jealous because he suspected his wife might have a lover, and he was worried that divorce might mean mum-of-two Arlene walking away with a chunk of his money.
"If you are not going to live with me, you are not going to be living with anybody," he fumed.