Akilov is due to appear in court at 10:00 am (0800 GMT) on Tuesday for a magistrate to decide whether to remand him in custody.
He had been denied residency in Sweden and had expressed sympathy for so-called Islamic State, according to police.
Police in Sweden's capital confirmed that a man had been arrested "on suspicion of a terrorist crime through murder" after the attack on Friday afternoon, in which a lorry was driven down a pedestrianised street in the capital before crashing into a department store.
Swedish Prime Minister Stefan Lofven, who led a nationwide minute of silence for the victims yesterday, said he was "frustrated" by the problem, while far-right Sweden Democrats leader Jimmie Akesson called it a "huge scandal". At least 15 people were injured in the incident. None of them have been identified. Police tried to find Akilov in February, but he had gone underground and was wanted by police, according to The New York Times. Agency head Benedicte Bjornland said it was likely the youth had been inspired by recent attacks in Stockholm, France, Germany, Britain and Russian Federation.
Sweden has always been known for its open-door policy toward migrants and refugees.
Earlier reports said that Swedish Police is suspecting that the man arrested in connection with the attack on a crowd of people in central Stockholm, to be the driver of the truck.
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"The efforts to locate (these people) is both time-consuming and resource-intensive", he said. But Swedish police chief Dan Eliasson said "there was nothing in the system that indicated that he would do anything like what happened on Friday".
"Do we somehow need a more repressive policy?"
Some 20,000 people gathered on Sergels Torg plaza on Sunday. His application was rejected a year ago. "I think it's very important to stay strong together against anything that wants to change our society, which is based on democracy", said one Swede who gave her name as Marianne.
The four dead were two Swedes - one of them an 11-year-old girl - a British man, and a Belgian woman. Their identities were not released by Swedish officials.
Mr Bevington lived in Stockholm with his family and worked as a director with music streaming service Spotify.
The Aftonbladet newspaper reported that he had said he was "pleased with what he had done". Nine of the wounded are still in hospital, two are in critical condition.