Zaw Lin and Wai Phyo killed Hannah Witheridge, 23, from Norfolk, and David Miller, 24, from Jersey, judges said.
The backpackers' bodies were found on a Koh Tao island beach in September 2014.
The defendants' lawyers say they will appeal. The accused retracted their initial confessions, saying police had tortured them. Mr Miller's brother said justice had now "been delivered".
Miss Witheridge's family said they needed time "to digest the outcome of the trial verdict".
At a Thai court in Koh Samui, three judges found the two bar workers - who were migrants from Myanmar - guilty of murder and ordered they face the death penalty.
Miss Witheridge and Mr Miller were found on a beach having been bludgeoned to death, and a post-mortem examination showed Miss Witheridge had been raped.
Prosecutors said DNA evidence collected from cigarette butts, a condom and the bodies of the victims, linked Lin and Phyo to the deaths.
By Jonathan Head, BBC South East Asia correspondent
The investigation has been a muddled affair.
The first officers on the scene were local police with apparently no idea how to seal off a crime scene.
Thailand forensic scientist Dr Pornthip Rojanasunand, whose institute was not allowed any involvement in the investigation, testified the crime scene had been poorly managed and evidence improperly collected.
Other flaws exposed during the trial included the police's failure to test Miss Witheridge's clothes or the alleged murder weapon for DNA.
The key question though, hung over one piece of evidence that did tie the defendants to the crime: the alleged match between their DNA and that recovered from semen found on Miss Witheridge's body.
The date of the original DNA analysis was said to have been 17 September, but the report submitted to court was dated 5 October - two days after police had announced a positive match. That unexplained discrepancy inevitably raises suspicion that perhaps the result was manipulated.
Read more from Jonathan: A flawed and muddled investigation
Lawyers defending the accused argued DNA from a garden hoe - allegedly used as the murder weapon - did not match samples taken from the men.
They also claimed evidence had been mishandled by police and the pair's confessions were the result of "systematic abuse" of migrants in the area.
Andy Hall, international affairs adviser for Migrant Worker Rights Network, which represented the men, said: "We strongly disagree with the decision of the court. This investigation was a shambles from the beginning.
"The defence team have had access to all the information in this case and the information we saw did not comply with international standards."
He said the defence team would mount an appeal in the case.
Hannah Witheridge, 23, was a University of Essex student from Hemsby, near Great Yarmouth in Norfolk.
Having earned a degree with first-class honours from the University of East Anglia she was working towards a masters degree in speech and language therapy in Essex. Her parents Tony and Sue, brother Paul and sisters Tania and Laura, described her as a "fun, vibrant and beautiful young woman" who had a love for animals.
The University of Essex has introduced an award for outstanding excellence in clinical placements in her memory. She "would have gone on to make a significant difference to the lives of many people", her family said.
David Miller, 24, from Jersey, had just completed a civil and structural engineering degree at the University of Leeds. He was described as a "bright, young man and a talented artist".
His friends and family held a memorial and commissioned a "simple seat from a plank of oak from a tree that fell in the great storm of 1987... This tree was another tower of Jersey strength brought crashing down before its time", they said.
His parents, Ian and Susan, and his brother Michael said: "Our 24 years of memories and his beaming smile will always be cherished. David was intelligent, hard-working, he was caring, inclusive, enthusiastic and fun. He irreplaceable to us."
Families talk of 'senseless' killings
The victims met on Koh Tao while staying in the same hotel.
The family of Mr Miller attended the hearing but relatives of Miss Witheridge did not travel to Thailand for the verdicts.
Her family said the verdict had left them "in the path of a whirlwind of emotions and difficulties".
In a statement they said: "The past year has served as an unimaginably impossible time for our family. We have found the trial process extremely difficult and our trips out to Thailand, to attend court, made for particularly distressing experiences.
"We found listening to proceedings very challenging and we have had to endure a lot of painful and confusing information. We now need time, as a family, to digest the outcome of the trial and figure out the most appropriate way to tell our story."
Speaking outside court, Mr Miller's brother Michael said: "We believe the result today represents justice for David and Hannah.
"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."
He said the Thai police investigation was "not the so-called shambles it was made out to be".
Mr Miller acknowledged that initially when Lin and Phyo were brought forward as suspects, the family was unsure.
"We saw images of two innocent-looking men surrounded by tough policemen. It was easy to conclude they might be convenient scapegoats.
"We believe that, after a difficult start, the Royal Thai police conducted a methodical and thorough investigation."
He added: "We hope the campaigners who have relentlessly promoted this case will respect the process of law and the decision of the court.
"[David] was hacked down from behind, dragged into the sea and left to die. That will live with us forever," he said.  He also paid tribute to relatives of Miss Witheridge for the "horrors they are also enduring with such dignity".
"Our lives have been changed forever."
Two Burmese men have been found guilty and sentenced to death for murdering two UK tourists in Thailand last year.