The family of Amrozi and Mukhlas also confirmed that the men had been executed on the prison island of Nusakambangan in central Java.
"Our family has received news of the execution... May our brothers, God willing, be invited by green birds to heaven now," Mohammad Chozin, a brother of the men, told reporters in Tenggulun, the men's home village in east Java.
Step Vaessen, Al Jazeera's correspondent in Tenggulun, said the farming village has a "very hardline" school in its centre.
"The school was founded by the father of the bombers. It is where the bombers grew up," she said.
"At the moment there are a lot of guests from hardline groups gathering at that school - they are waiting to attend the funeral. The police have cordoned off the whole village and they are stopped more hardliners from coming in. They are concerned about rioting and revenge bomb attacks."
The execution of the three convicted bombers is an attempt by the Indonesian government "to show that they are serious in their fight against terrorism," Vaessen said.
"The Bali bombers, who have always said they were happy to die as martyrs, have tried endlessly to postpone their execution with several appeals, even up to the constitutional court," she said.
"They have tried to escape the firing squad because they said that was against their human rights and they wanted to be beheaded instead. But they lost all appeals."
Two days ago the families of the men sent a letter to the Indonesian president to ask to for the execution to be delayed.
Peter Hughes, a survivor of the bombings, told Al Jazeera that the executions bring a sense of closure.
"This has been a long time coming. The guys are mass murders, they have caused a lot of grief to a lot of innocent people that were there having a good time," he said.
"The people that have supported the bombers need to have a think about what their real motives were, which was to kill a lot of people, they are certianly not heroes."
Security has been boosted across Indonesia amid fears of a backlash from a small minority who support the bombers.
"A lot of hardline groups have come to Tenggulun over the last couple of days to show their support and to be there at the [mens'] funeral," Vaessen reported.
"There is a lot of security. There are concerns about bomb threats and rioting taking place later in the day."
In recent days, police have investigated bomb threats received this week against the US and Australian embassies, and an internet letter purportedly written by the bombers threatening the life of Susilo Bambang Yudhoyono, the Indonesian president.
The convicted bombers had warned of retribution in a string of authorised media appearances from prison.
The condemned men had said they wanted to die as "martyrs".
The Indonesian anti-terrorist unit Detachment 88 was credited with capturing leaders of the Jemaah Islamiyah group - allegedly linked to the al-Qaeda network -and its military wing in a series of raids last year.