In the video the bombers seek to defend the attacks which left 20 people dead and many more injured.
Also on the tape are instructions for bomb-making.
The video, which has not been publicly released, was discovered after police raided a safe house that was recently used by Southeast Asia terror ringleader Noordin Mohamad Top in the Central Java city of Semarang on Wednesday, police said on Friday.
"The video contains the confession of the three suicide bombers explaining why they were prepared to carry out the suicide bombings," Indonesia's National Police Chief General Sutanto said.
The discovery of the video came just hours before police raided a house in neighbouring East Java province and killed Noordin's colleague and compatriot, bombmaker Azahari Husin.
Both men, thought to be leading members of the al-Qaida-linked Jemaah Islamiyah network, were blamed for planning last month's attacks as well as the October 2002 Bali bombings which killed 202 people.
Sutanto said two of the three bombers had been identified as Salik Firdaus and Misno, but gave no further details about them.
"The video contains the confession of the three suicide bombers explaining why they were prepared to carry out the suicide bombings"
National police chief,
Police on Thursday had identified two men only by their initials and said they were from Java island.
Police also found two bombs at Noordin's house, the police chief said.
Some 33 bombs were also found at Azahari's hideaway in the sleepy hill resort town of Batu.
"Those who carried out the October Bali bombings are linked to Azahari," Sutanto said.