The family of David Miller said the "correct verdict" has been reached after two Burmese migrants were sentenced to death for the murders of the backpacker and Hannah Witheridge in Thailand.
The battered bodies of Miss Witheridge, 23, and Mr 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 brutal killings but later retracted their statements, claiming they had been tortured by police.
At a court on the island of Koh Samui, the men were found guilty of murder and rape and issued with the death penalty.
Mr Miller's brother Michael, flanked by parents Ian and Sue, said outside court: "We believe the result today represents justice for David and Hannah.
"David always stood up for justice and justice is what has been delivered today.
"We respect this court and it's decision completely.
"It is our opinion that the evidence against Wai Phyo and Zaw Lin is absolutely overwhelming.
"They raped to satisfy their selfish desires and murdered to cover up that fact. They have shown no remorse during the trial.
"We believe the correct verdict has been reached."
The mothers of the two defendants burst into tears after the verdicts and emerged from court as Mr Miller's brother finished the family's statement.