"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 Dubai-based Gulf News newspaper said.
The three tourists, arrested on July 10, were accused of possessing and planning to sell more than one kilogram (2.2 pounds) of synthetic cannabis known as Spice. They were also accused of consuming drugs.
On Monday, the charges of selling drugs were modified to possessing and consuming drugs, according to Gulf News.
Britain-based campaign group Reprieve said the three men have been "subjected to torture including beatings and electric shocks" by police in the Gulf emirate.
"The central fact of this case remains that these men were tortured by police, but there has been no proper investigation into their abuse," Reprieve investigator Kate Higham said in a statement.
The group urged authorities in the United Arab Emirates "to grant these men clemency, release them and allow them to return home to their families".
Reprieve called for British Prime Minister David Cameron to push for this during Sheikh Khalifa's visit.
"It also remains essential that the UAE conduct an impartial investigation into these men's torture, and ensure it is never allowed to happen again."
Tracy Cameron, mother of Grant Cameron, described the jail term 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, which coincides with the holy Muslim month of Ramadan during which the Gulf country's leader usually grants amnesty to large numbers of prisoners, 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 (and) 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 UAE have dismissed the allegations, saying an internal investigation found them to be "baseless".
A spokesman for British premier Cameron confirmed Monday the issue would be raised during the UAE leader's visit.
"Clearly we have a state visit, we have an opportunity to build and strengthen relations between our two countries and as part of that we'll be talking about a wide range of issues which will include concern about these cases," he told reporters in London.
"The prime minister's clear there's no no-go areas in this.
"We've asked for a full, impartial and independent investigation into the incidents."
The case has also been taken up by campaign groups like Human Rights Watch and Amnesty International, which 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 April 19 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.