The high-voltage, direct current cable will form part of a new electricity highway - designed to carry excess wind or solar energy from Germany to Norwegian pump-storage plants.
Germany can only realise ambitious goals for increasing its renewable energy production if electricity can be stored on windy or sunny days for use on cloudy, still days.
But although Germany has impressive wind and solar photovoltaic generation capacity, it has no way of storing excess electricity.
Norway, on the other hand has a large number of pump-storage plants, where excess electricity is used to pump water uphill into high-altitude storage tanks. When energy is needed, the water is released, turning hydroelectric turbines and generating electricity on the way downhill.
The new connection could also be used to bring electricity back to Germany to meet shortfalls in supply, said grid operator firm Tennet.
The Dutch-German operator said the project details - which would see two direct current cables laid between the countries - would be agreed and signed by September.
"The first [cable] should be ready by 2018, as long as all the necessary permits are granted over the coming year and that material and manufacturing capacities are sufficient," said a Tennet spokesman. The second cable should be in operation by 2028.
German Economics Minister Philipp Rösler - who met the Norwegian Minister for Oil and Energy Ola Borten Moe in Berlin before Thursday’s announcement - said he expected the planned energy exchange with Norway to "strengthen the security of supply in Germany and reduce the price of electricity for consumers and businesses."
The connection would also play an important role in Germany's transition from nuclear to renewable energy, said Minister Rösler, helping to "integrate renewable energy" and stabilize the grid.
German state-owned bank KfW will put up 25-30 percent of the costs for the new connection, which will play a vital role in storing Germany's excess energy from renewable sources for a rainy day. The first cable alone will require investments of up to €2 billion.
Tennet has been in discussions with Norwegian grid operator Statnett over the project for more than two years. The Norwegian company, which will be responsible for half of the construction work, also announced plans for a future cable linking Norway to the UK, slated for completion in 2020.
"Together, the two cables will strengthen the North European electricity grid and the supply security in Norway," Norway's energy department said in a statement.
"The cables will be used for profitable trading of power, meaning electricity will flow to Norway when prices in Germany and the UK are lower than here. In the same way, we will export when prices are high abroad."