The transaction will boost Det norske's production capacity and cash flow in Norway, where its main asset today is a share in the future Johan Sverdrup North Sea oil field.
The operation of the massive oil field, which is expected to be expensive to develop, should start in 2019.
Both groups combined produced 84,000 barrels of oil equivalent per day (boed) in 2013 in Norway.
Det norske also announced that it would issue new shares for $500 million.
The sale, worth 1.5 billion euros, includes "the Marathon Oil-operated Alvheim floating production, storage and offloading vessel, 10 company-operated licenses and a number of non-operated licences on the Norwegian Continental Shelf in the North Sea," the US company said in a statement.
After the operation, Det norske is expected to become one of Europe's biggest independent oil companies.
Marathon Oil will also hand over 136 million barrels of oil equivalent per day in proved plus probable reserves.
The value of the deal is bigger than Det norske's market capitalization, worth $1.6 billion early on Monday on the Oslo stock exchange, after a 7.03-percent rise of its stocks' price.
The operation will be financed by a $2.75 billion loan provided by BNP Paribas, DNB, Nordea and SEB.
"The company's largest shareholder Aker Capital AS has pre-committed to subscribe for its 49.99 percent pro rata share of such rights issue. The remaining 50.01 percent is fully underwritten by a consortium of banks," the company said in a statement.
The Norwegian group hopes to close the deal in the fourth quarter, after the approval of competition authorities.
The amount is close to the $2.6 billion Marathon will pay for the acquisition of the retail and transport operations of US competitor Hess, announced on May 22nd.