Cambridge University-educated Rurik Jutting is serving a life sentence for the murder of Sumarti Ningsih, 23, and Seneng Mujiasih, 26, in his luxury apartment in 2014.
The former Bank of America employee spent days torturing one of the victims while on a cocaine-fuelled binge before stuffing her body into a suitcase left on his apartment balcony.
Jutting did not deny the killings but had sought to plead guilty to manslaughter, claiming diminished responsibility because he was under the influence of drugs and alcohol.
The jury unanimously found Jutting guilty of murder and he was sentenced to life in prison in November 2016.
Jutting's lawyer Gerard McCoy had appealed for a re-trial, arguing that the deputy judge, Michael Stuart-Moore, had "wrongly directed" the jury by narrowing down the scope of the defence case for diminished responsibility by saying only a psychiatric disorder could constitute an "abnormality of mind".
Mr McCoy said Jutting showed severe traits of psychiatric disorders, far beyond the normal range and was therefore not in control of his actions.
However, three court of appeal judges said in their judgement that Stuart-Moore had only offered direction to the jury as advice, without mandating it.
"There is no merit whatsoever in this ground of appeal," the judges said in their ruling.
Jutting's defence team had previously argued that cocaine and alcohol abuse, as well as personality disorders of sexual sadism and narcissism, had impaired his ability to control his behaviour.
The prosecution rejected this, stating Jutting was able to form judgements and exercise self-control before and after the killings, filming his torture of Ningsih on his mobile phone as well as hours of footage in which he discussed the murders, bingeing on cocaine and his graphic sexual fantasies.