Swedish authorities say the suspect had previously served a prison sentence in the Nordic nation, but have not released any specific details of the crime, nor length of sentence.
Sweden's Prime Minister Ulf Kristersson has attended a commemoration even in Brussels today, alongside his Belgian counterpart Alexander De Croo, for the victims of a a deadly attack that left two Swedish football fans dead on Monday night.
Islamic State has claimed responsibility for the attack, saying Swedes were targeted because of their country's membership in a global coalition fighting jihadists.
Belgian authorities say there are no indications the shooter, a 45-year-old radicalised Tunisian national who was in Belgium illegally, worked as part of a network.
"The lone wolf theory seems to be the closest to reality", said federal prosecutor Frédéric Van Leeuw.
The gunman, named by Belgian media as Abdesalem Lassoued, had his asylum application rejected in 2020 and was subject to an order to leave the country that was never executed.
PM De Croo has called for better enforcement of these decisions for those who are "not entitled to protection". Such an order "must become more binding", he said.
Gunman served prison sentence in Sweden
Swedish authorities say the gunman served a prison sentence in Sweden between 2012 and 2014.
However, the Swedish Migration Board would not specify which crime or offence he had been convicted of, nor the length of the sentence which had been given.
A spokesperson would only say the man had been transferred from Sweden "to another European country under the Dublin Regulation", which stipulates that migrants must apply for asylum in the European country where they first arrive.
The Swedish Prime Minister, Ulf Kristersson, said that, according to "all indications", this "terrorist attack" had targeted Sweden and Swedish citizens "simply because they are Swedish".
"Never in recent history have Sweden and Swedish interests been so threatened as they are today", he warned.
On 17 August, Sweden had to raise its terrorist risk alert level to four on a scale of five because of the tensions caused by the burning of copies of Islam's sacred text on its soil since the beginning of the year.