Police also said the coordinated attacks have claimed the life of a third bystander, with a man dying overnight from gunshot wounds to the head.
Spokesman Colonel M. Iqbal said a man who was previously identified as one of the perpetrators was a wanted man named Sugito who happened to be at the scene when the attacks unfolded on Jan 14.
"We initially said Sugito was a perpetrator. A witness saw him walking next to a perpetrator initialed D," Col Iqbal said at a media briefing.
"We first thought both were perpetrators. Our intelligence mapping revealed the name Sugito is on our wanted list who had intensively communicated with D."
Sugito lived in Kerawang, West Java, and worked as a courier. He was one of the seven people killed in Thursday's attacks and was identified by DNA tests on his family members.
Colonel Musyafak, head of police health and medical department, told the briefing that one of those wounded in the attacks had died on Saturday night.
Mr Rais Karna, a security officer at Bangkok Bank, was shot in the head and had been unconscious since he arrived at the hospital.
"He has not been conscious since he arrived at the hospital. We did surgeries to save him. He didn't make it," Col Musyafak said.
The Islamic State in Iraq and Syria (ISIS) group has claimed responsibility for the coordinated bomb and gun assault on Jakarta's central thoroughfare Thursday, which also left four suspected attackers and two other bystanders dead.
More than 20 others were wounded.
Indonesian authorities blame the attack on an ISIS faction made up of Malay-speaking Indonesians and Malaysians which is part of the extremist group's ruthless fight for a self-proclaimed caliphate in Syria and Iraq.
Indonesian police said on Saturday they had arrested 12 people in raids across the country, including a man they believe handled financing for the Jakarta attacks, money authorities allege came from ISIS.
One of the injured, Dutchman Yohanes Antonius Maria, 52, was transferred to a Singapore hospital on Saturday from Gatot Subroto army hospital in Jakarta.
Another victim, 44-year-old Austrian identified as Mr Marek, was to be transferred to Singapore around noon on Sunday, the Indonesian officials said.
"They both have had a stable condition and therefore it is safe to be transferred. They were inside the Starbucks cafe and sustained wounds from shrapnels from the bomb," Col Musyafak said.