The court had previously rejected an appeal by Amrozi Nurhasyim, Gufron's younger brother, who has also been sentenced to death over the bombings.
The three men had argued that their convictions were illegal because they were based on an anti-terror law passed after the attacks.
In 2004, Indonesia's Constitutional Court ruled that that law could not be applied retroactively, but senior officials at the time said that the ruling would not impact on the Bali bombing verdicts.
String of attacks
The three men admitted in court to planning and carrying out the attacks, which they have said were meant to punish the US and its Western allies for alleged atrocities in Afghanistan.
Indonesia, the world's most populous Muslim nation, has been hit by a string of bombings in recent years, with the attack on the resort island of Bali on October 12, 2002 being most deadly.
About 30 people were convicted of carrying out the twin nightclub attacks. At least two suspects remain at large.
The bombings are believed to have been carried out by members of Jemaah Islamiyah, a local network of fighters provided with money and expertise by al-Qaeda, according to police and former members of the group.
Amrozi, Imam Samudra, and Ali Gufron, who is also known as Mukhlas, are now expected to face execution by firing squad unless Susilo Bambang Yudhoyono, Indonesia's president, pardons them.
But a presidential pardon is considered unlikely given Indonesia's international interests in tackling groups such as Jemaah Islamiyah.
In any case, the men have said they will not seek a presidential pardon.
In a statement read out by their lawyers, the men said that if they were executed, their blood would "become the light for the faithful ones and burning hell fire for the infidels and hypocrites".
Spokesman Nurhadi gave no indication when the executions would be carried out.