Information gleaned by the signal intelligence agency can then be used as currency when trading data with other western countries.
Despite the headaches the bill has caused since entering parliament in 2007, the government has never revealed the true purpose of the law, SvD writes.
Several sources close to the Swedish intelligence community told the newspaper that the controversial new eavesdropping law was primarily intended to keep track of Russian communications.
"Our geographical position means that 80 percent of Russia's contacts with large parts of the world travel through cables in Sweden. That is the core of the issue," said one source.
"The most important reason for the law is that the government, the Armed Forces and other agencies need intelligence about Russia."
But neither former Prime Minister Göran Persson nor his successor Fredrik Reinfeldt have mentioned Sweden's desire to listen in on the neighbours.
FRA in its turn has wanted to keep its intentions quiet for as long as possible to prevent Russia from rerouting its computer and telecommunications systems.
Swedish-Finnish telecom giant TeliaSonera owns one of the world's largest fiber-optic cable networks, and company maps confirm that the vast majority of all cable traffic to and from Russia crosses Sweden's borders, SvD reports.
All Russian email and telephone calls, for example, pass through Sweden, regardless of whether the recipient is located in Berlin, Hong Kong, Kiev or New York. And 85 percent of Europe's broadband customers are connected in some way to TeliaSonera's network.
The new surveillance law will require all Swedish telecom operators to store any communications passing Swedish borders and make them available for FRA's perusal at collection nodes located at various points around the country.
TeliaSonera said it was currently considering ways to circumvent Sweden.
"Our aim is for international traffic and transit traffic to bypass Sweden," Malin Frenning, CEO of TeliaSonera International Carrier, told SvD.
But to construct a new network outside of Sweden would cost the company a lot of time and money. And there is also a risk that communications would then pass through other countries that have created laws similar to Sweden's, such as the Netherlands, the United Kingdom and Germany.