Michelle Palmer, 36, of Oakham, Rutland, and Vince Acors, 34, of Bromley, south-east London, were arrested on 5 July, but the pair had denied charges of public indecency and having unmarried sex.
They were fined 1,000 dirhams (Ģ160;$350) and will be deported after serving their sentences.
The pair were not at Dubai's Court of First Instance to hear the ruling but had been ordered not to leave the emirate.
Their defence lawyer Hassan Matter had insisted they would be proved innocent and said they were upset by the verdict.
"We are making an appeal against the verdict. They have not been arrested and taken into custody yet," he said.
"I have 15 days to appeal. I have to find the reason why the judge gave three months."
The pair were arrested on Jumeirah Beach hours after meeting at a champagne brunch at Dubai's five-star Le Meridien hotel.
A police officer told the court he had warned the pair about their inappropriate behaviour, but returned later to find them having sex on a sun lounger.
Palmer, who was sacked from her job in Dubai as a publishing executive after her arrest, said in a statement she and Acors had been "just kissing and hugging".
The pair's counsel Matter said during the trial, "The Public Prosecution failed to produce corroborative evidence against my clients concerning having consensual sex and committing indecent gestures in public."
Witness statements, including one from the police officer, were "wrong" and medical examinations had proved Palmer had not had sex on the beach, he maintained.
Friends of Palmer say she has been admitted to hospital in recent weeks suffering from anxiety and depression.
The case has turned the spotlight on the lifestyle of the 120,000 British residents of the United Arab Emirates.
The BBC's Christian Fraser says there have been concerns lately that tourists are ignoring the emirate's strict Islamic laws and that the outcome of this case will be a warning that such drunken behaviour will not be tolerated in public.
Other Britons too have been in trouble in Dubai, Sky News reports:
Tracy Wilkinson, 44, spent two months in prison after being found with traces of prescription drugs in her body.
Youth worker Andrew Brown, 43, was pardoned five months into a four-year jail term after a microscopic speck of cannabis was found on his shoe.
Radio 1 DJ Grooverider served 10 months of a four-year sentence for possessing cannabis in Dubai.