The man, who is from Uzbekistan, was arrested in the early hours of the morning after the terror attack left four people dead and 15 injured.
Speaking at the press conference in the Swedish capital Stockholm, Eliasson said he could not give any further details on the suspect or if he had any links to the ISIS terror group.
He said: 'He was known. The intelligence and security police were aware and said he was a marginal character.
'There is nothing that tells us that we have the wrong person.'
He added he did not know whether others were involved in the attack and said 'we cannot exclude this'.
It is not know how long the suspect had been in Sweden. Reports by Swedish media described him as a father of four who was found to have ISIS propaganda on his laptop.
Reports have also suggested that the suspect posted jihadist propaganda on social media and had pictures of injured people following the Boston Marathon explosion in 2013.