Prison officials said the three men refused blindfolds before facing the firing squad and all died instantly.
The executions are a highly sensitive issue in Muslim-majority Indonesia and had been delayed on several occasions.
However, most Indonesians are believed to have supported the death penalty for the bombers.
On Sunday the country's leading Islamic body, the Indonesian Council of Ulamas, announced that the three men could not be considered "martyrs".
|Foreign embassies say they fear reprisal attacks may follow the executions [Reuters]
"Someone who killed others will not die as martyrs unless they waged a war in the name of religion. They were not fighting for religion," Umar Shihab, the head of the council, was quoted as saying by the Detikcom news website.
Several foreign embassies, including the US and Australia, have warned their nationals in Indonesia to keep a low profile amid fears that reprisal attacks could follow the executions.
"We advise you to reconsider your need to travel to Indonesia, including Bali, at this time due to the very high threat of terrorist attack," a notice posted on the Australian Department of Foreign Affairs and Trade website said.
Anyone travelling to Indonesia "should exercise extreme caution" it added, noting that Indonesian authorities have warned that attacks may include attempts to kidnap foreigners.
The 2002 bomb attacks on Bali were allegedly planned and funded by Jemaah Islamiyah – a South-East Asian group that Western and Indonesian intelligence agencies believe has close ties to al-Qaeda.