Two sources who had worked with the suspect, Rakhmat Akilov, independently identified him to Reuters from images distributed by police as the manhunt got underway on Friday.
Two police spokespersons declined to confirm his identity as did the suspect's court-appointed lawyer.
Thousands gathered in the spring sunshine near the site of Friday's attack to show support for those killed or injured when a hijacked beer delivery truck hurtled down a busy shopping street before crashing into a store and catching fire. The Uzbek man was arrested several hours later.
"The suspect had expressed sympathy for extremist organisations, among them IS," Jonas Hysing, chief of national police operations, told a news conference, using an acronym for the ultra-hardline militant group.
Two of those killed were Swedes, one was a British citizen and the other from Belgium, Hysing said of the attack, which echoes the earlier use of vehicles as deadly weapons in Nice, Berlin and London. Those attacks were claimed by Islamic State, but there has been no such claim yet for the Stockholm assault.
The suspect, aged 39 and from the Central Asian republic of Uzbekistan, applied for permanent residence in Sweden in 2014. However, his bid was rejected and he was wanted for disregarding a deportation order, Hysing said.
Security Police spokesman Simon Bynert said the suspect had been involved in an asylum process in Sweden, but that the security police had not been part of it.
Police had been looking for him since Sweden's Migration Agency in December gave him four weeks to leave, but security services had not viewed him as a militant threat.
Sweden's prosecution authority said a second person had been arrested on suspicion of having committed a terrorist offence through murder, but police said they were more convinced than ever that the Uzbek man was the driver of the truck.
Another five people were being held for questioning after raids and police said they had conducted about 500 interviews.
Police across the Nordic region went on heightened alert after the attack and in neighbouring Norway police set off a controlled explosion of a "bomb-like device" in central Oslo on Sunday and took a suspect into custody.
Although nine of the 15 people injured remained in hospital, two in intensive care, Stockholm began to return to normalon Sunday with the removal of police barricades along the Drottninggatan street where the attack took place.
Hundreds of flower bouquets covered steps leading down to the square next to where the truck ploughed into the Ahlens department store, with more piled up under boarded-up windows.
Only yards from the scene, thousands of people gathered in the Sergels Torg square in a show of unity as heavily armed police stood guard and a police helicopter hovered overhead.
"I want to show I'm not afraid to go out," Eva Udd, a 55-year-old nurse who had joined the demonstration with a friend, said. "I usually never go to things like this, but this just felt so very important."
Husam Kranda, a Libyan living in Sweden for the past five years and now working as translator, was among the multi-ethnic gathering which underlined Stockholm's cosmopolitan inhabitants.
"We believe it's our duty to come here and show our support for the Swedish society," he said.
"I know it's a difficult time, there is a lot going on within Swedish society and internationally. But today is not about that, it's about showing support for our neighbours and our beloved ones."
He was joined by his wife from Uzbekistan, Irana Mamedova.
"I really feel ashamed [of] that man, because this country give him everything, this country give him peace," she said of the Uzbek suspect. "He is a monster."
Prime Minister Stefan Lofven, addressing a Social Democratic party conference in the western city of Gothenburg, said Sweden would never be broken by acts of terror.
"We will hunt down these murderers with the full power of Sweden's democracy. There will be no compromises," he said.
Sweden, a nation of 10 million inhabitants, has long taken pride in its tolerant liberal society and been among the world's most welcoming nations to immigrants.
But some Swedes are having second thoughts after more than 160,000 people, many from Syria, applied for asylum in 2015.
The Ahlens store cancelled a planned half-price sale of smoke-damaged goods and apologised after a storm of protest on social media that this would be disrespectful to the victims.