The executions were carried out by firing squad early in a prison after a top court rejected an appeal filed by the three against their conviction, said the country's Attorney-General Ahmed al-Hamdi.
The bodies of the three were transported to a heavily guarded graveyard and the families were ordered to attend the burial, relatives said.
The case dates back to March 2014 when three policemen, including an Emirati officer, were killed in a bomb attack in Sanabis village, a suburb of the capital Manama.
Al-Ashter Brigades, a little-known group, claimed responsibility for the bombing.
Three suspects from Bahrain's Shiite Muslim majority were later found guilty of involvement in the attack.
In February, 2015, a Bahraini court sentenced the three to death.
The convicts claimed that their confessions were obtained under torture.
On Monday, the Bahraini Upper Court rejected the final appeal and upheld the death sentences for the three men: Sami Mushaima, 42; Abbas al-Samea, 27; and Ali Abdulshaheed al-Singace, 21.
The executions were carried out a day after clashes between security forces and anti-government protesters in Manama.
Rumours of the executions prior to the official announcement sparked an outcry from the opposition and human rights groups that warned such a move could further inflame the unrest in the country.
“This is a black day in Bahrain's history,” Sayed Ahmed Alwadaei, an official at the London-based Bahrain Institute for Rights and Democracy, said in a statement.
“The government of Bahrain knew about the torture of the three,” he added.
“It has been the subject of complaints and was raised by the defence in their trials, and been utterly ignored.”
Home to the US Navy's 5th Fleet, the small Gulf monarchy has seen a rise in violence since 2011, when mass protests led by the country's Shiites erupted in demands for wider reforms from the ruling Sunni family.
The protests, inspired by the Arab Spring revolts, were quelled with the help of regional Sunni powers, including Saudi Arabia.