Police had detained the man earlier on Friday in the wake of the attack.
Nine victims were left in a serious condition and reports suggested a pram was caught in the path of destruction.
"One person has been arrested on suspicion of terrorist crimes through murder", a spokesperson at the prosecutors office said.
"We continue to investigate at full force", Evensson said, urging people not to go to central Stockholm on Friday night.
More recently, 12 people lost their lives in Berlin when a truck rammed shoppers at a Christmas market in the German capital.
"People were screaming and running in all directions", said Brandon Sekitto, who was in his auto nearby.
More than 80 victims were killed in France after a terrorist drove a truck into crowds that were celebrating Bastille Day in Nice last July.
Swedish broadcaster SVT said shots were fired at the scene, though it wasn't clear by whom and police said they could not confirm that.
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Detectives arrested the man after issuing a picture of an individual they wished to speak to, later saying he matched the description of the image.
A manhunt is under way for the driver of the vehicle, who police said is still at large.
Officials said they are unsure whether the attack was an isolated event or whether more attacks are to come.
"Then it drove into a pillar at (department store) Ahlens City, where the hood started burning".
Mr Lofven spoke to police officer Jonas Hvitfeldt, who was guarding a cordon outside the store.
"We have police positioned at several strategic places with a particular risk threat".
Last month, Khalid Masood, a 52-year-old convert to Islam known to British security services, drove a auto at high speed into pedestrians on London's Westminster Bridge before launching a frenzied knife attack on a policeman guarding the parliament building.
External Affairs Minister Sushma Swaraj on Friday reflected on the terror attack near the Indian Embassy in Stockholm and said that she was in touch with the Indian Ambassador in Sweden.
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The lorry smashed through stone lion bollards into the pedestrianised area, leaving a trail of blood and debris. "I don't know if the other one made it", Sidi said. "Heavy weapons, civilian police, etc", he said. "There were bodies on the ground everywhere", she told the BBC.
Sadiq Khan said it appears Sweden has "seen a despicable act of terrorism aimed at harming innocent people and attacking our shared values of democracy, freedom, justice and tolerance".
"There was, just outside the store, there was a dead dog, the owner screaming, there was a lady lying with a severed foot".
"There was a sense of panic, people standing by their loved ones, but also people running away".
"Sweden has been attacked", Lofven wrote in a Twitter post. "This indicates that it is an act of terror". No one else was killed.
Abdulwahab rigged a auto with explosives in the hope that the blast would drive people to Drottninggatan - the street hit Friday - where he would set off devices strapped to his chest and back. The vehicle bomb never went off, and he died when one of his devices exploded among Christmas shoppers.
Another man was detained in a large-scale police operation in the immigrant-heavy Hjulsta neighborhood north of Stockholm, the Expressen newspaper reported.
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