"The Swedish Civil Aviation Authority has decided to issue a traffic permit to Viking Airlines for regular flights from Sweden to Arbil in Iraq," the agency said in a statement.
"We will resume the flights shortly," Viking Airlines said in a separate statement, adding that "initially, we will operate from Stockholm and Copenhagen."
The Swedish aviation authority grounded all Swedish flights to Iraq on August 10, a day after the pilots of a Nordic Airways MD-83 aircraft reported seeing flashes of light after taking off from Sulaimaniyah Airport in northern Iraq.
Aviation officials from Iraq's Kurdish region have dismissed reports that the airliner was targeted, but Swedish officials said there was no doubt the airliner had been fired upon.
"We can't prove it, but we have three people in the cockpit who said they saw it. It is clear that it was some form of shelling. But we don't know if they (the attackers) knew it was a Swedish plane," he told AFP at the time.
He said the plane was at an altitude of 1,400 metres (4,500 feet) when the incident occurred.
Viking Airlines and Nordic Airways, which at the time were the only Swedish carriers flying to Iraq, had along with several other companies applied to resume flights to the north of the country.
Viking Airlines was however the only firm to receive authorisation.
"Our decision was based on among other things the Foreign Ministry's report on the security situation in the area and on a security analysis from the airline," the aviation authority said, adding that the permit was good until March 29 and would be retracted if the situation in the region worsened.
The flights cater to the many Iraqis in Sweden, the European country that currently takes in the most refugees from the wartorn country.