Senior Commissioner Martinus Sitompul, head of public relations for the Indonesian National Police, named the two bombers as Ahmad Sukri and Ikhwan during a press briefing Friday. No other immediate details were given.
CNN affiliate CNN Indonesia is reporting that a further three individuals have been arrested in connection with the attack.
The bombings, which took place at a bus station in the Indonesian capital, killed at least three police officers and wounded six officers and five civilians, national police spokesman Inspector General Setyo Wasisto told reporters Thursday.
Aluminium, nails, buckshot and receipts for purchasing rice cookers were found at the scene of the bombing, Wasisto said.
It's not clear who carried out the attack but Sitompul said authorities suspect ISIS involvement, according to CNN Indonesia.
In the past, ISIS has claimed responsibility for terror attacks in the Southeast Asian nation.
"The Islamic State remains the main driver of attacks in Indonesia, and the threat posed by militants linked to the group is likely to escalate in the country," Otso Iho, senior analyst at Jane's Terrorism and Insurgency Center, said in a statement.
"People who have traveled to join the Islamic State in Iraq and Syria (will) begin to return back to their home countries. Experienced returning militants will be able to provide combat training."
The attack came two days before the start of Ramadan. Many of those caught up in the attack had been involved in a torch parade celebrating the start of the Islamic holy month.
Indonesian President Joko Widodo issued a statement Thursday said the perpetrators of the attack would be hunted "down to the root."
"The attack is indiscriminate. It is outrageous. The victims are motorbike taxi drivers, microbus drivers, street vendors policemen ... I call for the nation to remain calm and to maintain unity," he said.
Teten Masduki, chief of staff to the president, visited the victims of the attack at the Premier hospital on Thursday morning to give his condolences.
Last year, ISIS said it carried out a suicide bombing and shooting near a Starbucks in Jakarta
. Two people were killed, and 24 were wounded.
Police said an ISIS militant based in Syria ordered his operatives to carry out that attack.
Indonesia is the world's most populous Muslim country. In recent years it has been fighting against radical extremism as ISIS attempts to recruit members within the country.
Some Indonesian teachers have instructed students on how to avoid extremist ideology.
Malaysian Prime Minister Najib Razak said Wednesday on his official Twitter that he was "disgusted" by the Jakarta attack.
"Malaysians stand with the Indonesian people at this time. Terrorism has no borders, knows no race or creed," he said.