Imam Samudra, Amrozi Nurhasyim, and Ali Ghufron, sentenced to death five years ago for the attacks, have exhausted their appeals and were recently told they would face a firing squad in November.
The men have publicly said that they hope their deaths will spark revenge attacks in Indonesia.
The US embassy in the capital Jakarta issued a warning on Friday that Western interests could be targeted and urged American citizens to exercise caution.
Natapawira warned that shopping centres, bus terminals, railways stations and places of worship were all possible targets.
Police said they had found and defused two bombs in a Balinese Hindu migrant area on Sulawesi island on Wednesday and Thursday.
"I think there is a connection between this and the execution of Amrozi and others," Suparni Parto, a local police chief, told the AFP news agency.
Protests are expected to be held near the prison island of Nusakambangan off
southern Java where the three men are being held awaiting execution.
About 1,000 police, including an elite mobile brigade and anti-terrorism officers, have been sent to the nearby town of Cilacap.
"I think most Indonesians will greet the executions with a sigh of relief, that its finally over. And the world at large will have a similar reaction," Sidney Jones of the International Crisis Group think-tank told Al Jazeera.
|The bombings targeted nightclubs on the resort island of Bali [File: AFP]
"I think its been an appalling circus over the last few months and if there is any security risk its partly because the Indonesian government allowed these men to have access to the media where they could issue their threats over and over again."
The bombings in 2002 targeted nightclubs on the predominantly Hindu island of Bali and more than 160 foreigners were among the victims.
Amrozi, Mukhlas and Imam Samudra have said that the attack was a response to the US-led invasion of Afghanistan.
Jemaah Islamiyah, the Southeast Asian group which the three men were believed to have been part of, have also been blamed for at least three other suicide bombings in Indonesia since the Bali attacks.
In 2005, at least 21 people were killed in a series of blasts in cafes and restaurants in Bali.