Justice and Immigration Minister Morgan Johansson wrote in a debate article in newspaper Dagens Nyheter on Thursday that the investigator will present the findings, and a proposal for law changes, by 18 June 2015.
The new investigator, Lars Werkström, works as a legal council at the Swedish Prosecution Authority.
The starting point for Werkström's investigation is a UN Security Council resolution from late September 2014. That resolution requires all UN member states to have laws making it possible to prosecute and punish people, in a way that reflect the seriousness of terrorism.
At least 110 people from Sweden have travelled to Syria or Iraq to fight in al-Qaida-inspired groups, according to Swedish secret police Säpo.