The blasts -- at least six, according to eyewitnesses -- were close to a shopping centre, the Sarinah.
Graphic photographs from the scene showed the bloodied bodies of what appeared to be two men in civilian clothes lying by the side of a road next to the wrecked police post.
Ruli Koestaman, 32, who had been in a meeting in a nearby building, said the attack started around 10:35am (0335 GMT).
As well as the known deaths, a number of people were feared injured in Thursday's assault, with an eyewitness telling AFP he had seen a \"terrorist\" open fire on a local journalist.
A security crackdown weakened the most dangerous extremist networks, leading to a long lull in large-scale strikes. However, the emergence of Islamic State has raised concern that Indonesians returning from Middle East battlefields could stage attacks on home soil.
Indonesia, the world's most populous Muslim-majority country, suffered several major bomb attacks by Islamic radicals between 2000 and 2009, including the 2002 bombings on the resort island of Bali that killed 202 people.
'Four people died, one police officer and three civilians,' national police spokesman Anton Charliyan said.
Badly mangled bodies were seen lying on the streets as security forces moved in, with regular reports of gunfire and warnings of snipers in the area.
Witnesses said at least one gunman had attacked a cafe in the city centre -- near a cluster of embassies -- shooting at bystanders, as a series of explosions rocked the area.
Gunfire and explosions in the Indonesian capital Jakarta killed at least four people Thursday, with police flooding the streets amid fears gun-toting militants were still on the run.
Indonesian police say the attackers may be linked to ISIS.