The battered bodies of Hannah Witheridge, 23, and University of Leeds student David Miller, 24, were discovered on the idyllic holiday island of Koh Tao on September 15 last year.
Bar workers Zaw Lin and Wai Phyo, also known as Win Zaw Htun, initially confessed to the killings but later retracted their statements, claiming they had been tortured by police.
At a court in Koh Samui last December, three judges found the men guilty of murder and ordered that they face the death penalty.
But since then, seven Thai lawyers and a team of international advisors were said to have been working to exonerate the Burmese pair.
Their appeals against their convictions and sentences were reported to have been lodged this morning.
Prosecutors claimed DNA evidence collected from cigarette butts, a condom and the bodies of the victims linked Lin and Phyo to the killings.
But lawyers representing the pair, both 22, said DNA samples from the alleged murder weapon – a garden hoe – did not match that of the two men.
The defence team said DNA evidence was mishandled by police and the defendants’ confessions were a result of torture in the context of “systematic abuse” of migrants on Koh Tao.
A bizarre reenactment of the murders in which the defendants were paraded in front of the media was also “staged under threat of violence”, the lawyers added.
Thai police denied using force during their investigation.
Miss Witheridge, a University of Essex student from Hemsby, Norfolk, and Mr Miller, of Jersey, who had just completed a civil and structural engineering degree at Leeds, met on Koh Tao while staying at the same hotel.
Post-mortem examinations showed that both had suffered severe head wounds.
Miss Witheridge had been raped while Mr Miller died after being hit over the head before drowning in the sea.