The three faced the firing squad, a week after a court upheld their death sentences over a bomb attack in March 2014, the prosecution said in a statement carried by BNA state news agency.
The executions came a day after demonstrations broke out across Shiite villages following rumours that the authorities were going to execute the three men.
They are the first in six years in the Gulf kingdom, according to London-based human rights group, Reprieve, which had warned on Saturday against the move.
"No, no to execution," the protesters chanted.
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The high court on Monday upheld the death sentences against the trio convicted in a bomb attack in March 2014, which killed three policemen, including the officer from the United Arab Emirates.
Seven other defendants received life terms.
The Emirati officer was part of a Saudi-led Gulf force which rolled into Bahrain in March 2011 to help security forces put down a month of protests led by the country's Shiite majority.
Brian Dooley, head of the Washington-based Human Rights Defenders, said if the executions were carried out it "would be a new, enormously alarming step from Bahrain's regime".
"Washington should warn its Gulf ally that this would be a reckless, frightening level of repression to pursue, likely to spark rage and further violence in an already volatile region," he said in a statement.
Bahrain is a strategic ally of the United States and home to the US Navy's Fifth Fleet.