Chief prosecutor Tomas Lindstrand said police were "98% sure" that the man was Iraq-born Taimour Abdulwahab al-Abdaly.
Abdaly, 28, is believed to have died minutes after setting off a car bomb on Saturday. Two other people were hurt.
Seven US FBI bomb experts are heading to Stockholm to help the investigation, Sweden's intelligence agency said.
Although Abdaly was a Swedish citizen, he had been living in the UK.
British police have been searching a house in Luton, north of London, where Abdaly lived.
Mr Lindstrand said Swedish police were now trying to work out what the bomber's target had been before he blew himself up prematurely.
"He had a bomb belt on him, he had a backpack with a bomb and he was carrying an object that has been compared to a pressure cooker. If it had all blown up at the same time, it would have been very powerful," he said.
A car containing gas canisters blew up first in a busy shopping street in the area of Drottninggatan at 1700 local time (1600 GMT) followed minutes later by a explosion in a street about 300m (985ft) away that killed the bomber.
Abdaly was named as the registered owner of the car.
Mr Lindstrand said they believed the bomber had intended to kill "as many people as possible".
"Where he was headed... we don't know," he said.
"It is likely that something happened, that he made some kind of mistake [and] part of the bombs he was carrying went off and caused his death.
"This was during Christmas shopping in central Stockholm and he was extremely well-equipped when it came to bomb material. It is not much of a stretch to say he was going to a place with as many people as possible."
Mr Lindstrand said possible targets included the city's central train station or to Aahlens, a popular department store.
In a profile on the Muslim dating website Muslima, Abdaly said he was born in Baghdad and moved to Sweden in 1992, before arriving in the UK in 2001 to study.
He said he had got married in 2004 and had two young daughters.
"I want to get married again, and would like to have a big family. My wife agreed to this," he wrote.
Mr Lindstrand said Abdaly was completely unknown to Swedish security services before the blasts.
However, he pointed out: "He didn't live in Sweden; he lived in the UK. He left Sweden maybe 10 years ago."
Meanwhile, British police have been searching Abdaly's house in Luton. His wife and children are reported to live in the UK, although their exact whereabouts are not known.
It has emerged that Abdaly had attended the Luton Islamic Centre but left after other members accused him of having a "distorted view" of Islam.
A Swedish news agency has released an audio recording apparently made by Abdaly, in which he says oppression against Muslims in Europe will not be tolerated.
He refers to drawings of the Prophet Muhammad and to the presence of foreign soldiers - including Swedes - in Afghanistan.
If confirmed as a suicide bombing, the attack would be the first of its kind in Sweden.
In pictures: Stockholm blasts
Sweden's Prime Minister Fredrik Reinfeldt has said the attacks are unacceptable in Sweden's "open society", which he said was a democracy that respected different cultures.
The blast appears to have been of the same relatively unsophisticated nature as recent attempted attacks in New York, Glasgow and London, says BBC security correspondent Nick Childs.
Such attacks, carried out by individuals, are especially hard for the security agencies to trace and are an increasing cause for concern, he adds.

Emergency services were called to the Fernways unit on Cecil Road, Ilford, at about 22:20 BST on Saturday to reports of an assault.
Two people found with stab wounds were pronounced dead at the scene.
A 50-year-old man was arrested on suspicion of murder and is in custody at an east London police station.
Police believe the victims and the man arrested knew each other, but said they were not related and were not staff at the unit, which is part of the care provision of Redbridge Borough Council.
Officers say they know the identities of the deceased and their next of kin have been informed.
Post-mortem examinations on the pair will be held later, the Met said.
A man who blew himself up in Stockholm was carrying three explosive devices and intended to kill as many people as possible, prosecutors say.
[NEXT_CONCEPT]
A woman in her 50s and a man in his 80s have been stabbed to death at a sheltered housing unit in north-east London.