The company is to be charged with operating the rail service between Malmö and Copenhagen, checking tickets and maintaining the trains - tasks that it currently shares with SJ.
The contract also includes the operation of the Danish coastal rail service up to Helsingör, traffic between Malmö and the borders of the Skåne region, as well as a route through Blekinge to Karlskrona.
As the winner of the highly competitive bidding battle, DSB also has an option to extend the Öresund service to incorporate Gothenburg, Växjö and Halmstad, as well as traffic between Hässleholm and Halmstad.
The Danish company has promised to increase the number of trains on the routes in question, news agency Ritzau reports.
DSB and its partner First Group have indicated that they will create separate companies on either side of the bridge. In Sweden, the company is to be called Öresundstrafiken, while its Danish counterpart will go under the name Kystbanan.