The Appeal Court rejected the case presented by lawyers representing Zaw Lin and Win Zaw Htun, who used the mishandling of evidence by police, including images and documents, to argue for a reversal of the judgement.
The Criminal Court convicted and sentenced them to death on Dec 24, 2015.
The process leading to the indictment of the two migrants had been completed, according to the Appeal Court ruling read out in Koh Samui court on Wednesday.
Zaw Lin and Win Zaw Htun were not present for the hearing. They are serving their sentence in Bang Kwang Prison in Nonthaburi. Theerawut Prammahant, the deputy prosecutor for Koh Samui, heard the ruling on their behalf.
The two were sentenced for the murder of backpackers Hannah Witheridge and David Miller on the island in Surat Thani province on Sept 15, 2014.
Witheridge, 23, was raped and bludgeoned to death and Miller, 24, died from blows to his head.
The two Myanmar migrants denied the charges.
The case sparked controversy as their lawyers, human rights activist and family members claimed they were scapegoats, pointing to alleged mishandling of evidence, but police insisted they had arrested the right people.