Officials originally believed there were five attackers, but later said one man thought to be a militant was actually a civilian.
All of the attackers, including two previously convicted militants, were killed.
ISIS has claimed it carried out the attacks.
At least 20 people were injured, several of them in a serious condition.
One of the militants seen carrying a gun and rucksack during the attacks was named as Afif Sunakim. He was previously given a seven-year jail term for attending a militant camp.
The others have been identified as Dian Joni Kurniadi, M Ali, and Ahmad Muhazan bin Saron.
The attacks began with a series of bomb blasts at an intersection near a shopping mall and a Starbucks coffee shop. As people inside ran out, two gunmen waiting outside opened fire.
At least two militants also attacked the police box in the centre of the intersection in a suicide bomb attack.
The attackers planned to target government offices and foreigners in other Indonesian cities, a spokesman said.
So far, 12 arrests have been made and police have also shut down at least 11 websites and social media accounts.
The attackers are thought to have belonged to an ISIS faction made up mainly of Indonesians and Malaysians. The guns they used came from the Philippines, officials said.
Hundreds of people from Southeast Asian countries with significant Muslim populations have travelled to Syria and Iraq to fight with the group.
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