The sentencing of Grant Cameron, Karl Williams and Suneet Jeerth, all 25, came a day ahead of a visit by UAE President Sheikh Khalifa bin Zayed al-Nahayan to Britain, during which the case is expected to be discussed.
"The presiding judge Ali Atiyyah Saad of Dubai Court of First Instance said the trio will be deported after serving four years in jail," the website of Gulf News newspaper said.
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Britain-based group Reprieve said the three men have been "subjected to torture including beatings and electric shocks" by police in the Gulf emirate.
The three tourists, arrested on July 10, were accused of possessing and planning to sell more than one kilogram of synthetic cannabis known as Spice. They were also accused of consuming drugs.
On Monday, the drug selling charges were modified to possessing and consuming drugs, according to Gulf News.
The three denied they planned to sell the drug, Gulf News said.
Tracy Cameron, the mother of one of the men, Grant Cameron, described the jail term Monday as "very, very positive news", telling British media that they had been warned to expect a 15-year term.
She said she hoped the 25-year-old and his friends would be pardoned in July and could be home by the end of the year.
"Grant has always pleaded not guilty and his evidence has been pretty consistent throughout from the moment his initial first statement was taken," she told BBC television.
"We have to bear in mind that all three boys were forced to sign documents in Arabic, the information is pretty inconsistent that the UAE authorities showed as evidence in the courtroom."
"I am very positive that my son will be home with his family by the end of the year at the very latest."
On Sunday, Cameron's mother described the three men's "terrifying ordeal" after their arrest, saying they were beaten and given electric shocks.
Authorities in the United Arab Emirates have dismissed the allegations, saying an internal investigation found them to be "baseless".
But the British government is pushing for an independent investigation into the claims, which it says it takes "extremely seriously".
"We have raised, and continue to raise, these allegations at the most senior levels in person and through diplomatic channels, including through ministers," a Foreign Office spokesman said.
The case of the three Britons has been taken up by campaign groups including Human Rights Watch and Amnesty International, who also want London to press Sheikh Khalifa on the treatment of dissidents.
The human rights situation in the UAE has come under much criticism lately with the Gulf country trying dozens of Islamists for allegedly plotting to seize power.
An earlier assessment report by the US State Department accused Emirati authorities of "arbitrary arrests, incommunicado detentions, and lengthy pretrial detentions; limitations on citizens' civil liberties... and citizens' inability to change their government."
The UAE foreign ministry criticised Washington's report as "unbalanced", while insisting the Gulf federation is committed to bettering its rights record.
Sheikh Khalifa will stay at Windsor Castle as a guest of Queen Elizabeth II and will also meet with British Prime Minister David Cameron.
