Svensson went on loan from the Danish league last winter and a purchase option was written into the agreement with Dortmund.
It is now being utilized.
The transfer is being showcased on the club's website.
"Daniel has fully and from day one lived up to the expectations we had for him. His flexibility suits our game very well and gives us many alternatives. Moreover, Daniel is also a great guy and exemplary professional," says sports manager Sebastian Kehl.
For his part, Svensson says:
"I have been very well received here and have quickly integrated into the team. I am very happy to continue playing for Borussia Dortmund. It is a big club with fantastic fans. My goal is that we will celebrate successes together here. I will work hard every day to achieve that."
German media reports that the transfer sum is somewhere around 80 million kronor.
Borussia Dortmund has made a strong surge in the league and lies fifth before the weekend's final round, with a Champions League spot within reach. The club concludes at home against already relegated Kiel.
Svensson missed the opportunity to participate in the national team's friendly matches against Luxembourg and Northern Ireland in March due to injury. On Tuesday next week, national team coach Jon Dahl Tomasson selects the squad for the friendly matches against Hungary and Algeria in early June.
