One of his lawyers, Qadhar Faisal, said on Thursday that Samudra would fight the decision because it was not based on Islamic law.
"After all legal avenues have been exhausted, he will accept the death penalty," Faisal said.
He added Samudra would lodge his appeal when he was officially notified that the Bali high court had rejected his original appeal.
Imam Samudra is the second key bomber on death row to have his appeal rejected by the Bali high court. The other man, Amrozi, is also appealing to the Supreme Court.
Investigators believe Samudra is a leading member of the Jemaah Islamiyah group, which staged the attack on two crowded Bali nightclubs to avenge Western oppression of Muslims worldwide.
The Bali blast killed 202 people
The bombings on 12 October, 2002, killed 202 people, mostly Western holidaymakers.
The Afghanistan-trained Samudra once said he would welcome death as it would bring him closer to God.
Samudra, 33, was convicted of attending planning meetings, selecting the blast targets in Bali and assigning tasks to the bombers.
A third bomber called Mukhlas is also on death row and has also said he will appeal. A fourth key bomber called Ali Imron escaped with a life sentence after expressing remorse.