The alliance's signature was overseen personally by Vladimir Putin in advance of his return to a third Kremlin in which Russia's stalling oil production will one of his biggest concerns.
"We value our relations with our neighbours and are confident that the project will develop well," news agencies quoted Putin as saying at the ceremony.
"There is no question that it will not have the government's full support," Putin added.
The deal will see Norway's state-held group win one-third ownership in a new joint venture that will explore one of the Russian firm's many fields in the Barents Sea.
The agreement also covers three Rosneft blocs in the Far Eastern Sea of Okhotsk.
Rosneft said it should be able to acquire stakes in undisclosed Statoil international projects in return and also explore section of the Norwegian part of the Barents Sea.
"This agreement is at the core of our strategy, supporting our long-term growth ambitions," said Statoil CEO Helge Lund.
The pact's structure is almost identical to those Rosneft engineered in the past month with the US supermajor ExxonMobil and Italy's ENI.
All three alliances give foreign companies access to the Arctic in return for investments in development and advanced technology sharing with Rosneft.
Statoil said it also hoped to use its experience to help Rosneft tap a vast undeveloped field in West Siberia and tackle an untouched shale oil deposit in the central Stavropol region.
Rosneft President Eduard Khudainatov said he expected Statoil to invest $1 billion in the Arctic bloc while spending the rest on the Sea of Okhotsk.
He added that the two firms' overall investment "in case the (energy) resources are confirmed" could reach up to $100 billion over the coming decades.
The deal represents another massive coup for Russia's energy tsar Igor Sechin — a former Rosneft chairman and close Putin ally who is widely tipped for a promotion in the new government.
One of Russia's most secretive but effective ministers was a key player in the government's campaign against the now-jailed tycoon Mikhail Khodorkovsky's huge private oil firm Yukos.
Rosneft scooped up the biggest field held by Yukos at a discount when Khodorkovsky's firm was broken up in 2004 and has since grown into a powerhouse that produces one-fifth of all the country's oil.
The three alliances it sealed since last month also underscore how the interests of the Kremlin coincide with those of the world's largest energy firms.
Russia's status as the world's largest oil producer is becoming imperilled by gradually slowing extraction rates in its Soviet-era Western Siberia fields.
But new field development in Eastern Siberia — a remote region with limited current pipeline access — has been prohibitively expensive and at-times disappointing in terms of the quality and amounts of oil found.
A more committed strategy toward Arctic development began to emerge last year when Rosneft tried but failed to strike a historic alliance with BP of Britain.
But foreign interest in the Arctic continues to mount, despite the decades it will take to develop the virgin territory, because of uncertainty in the Middle East and the nationalization drives of Latin American states such as Venezuela.
Putin last month vowed to win $500 billion in investment for offshore field development over 30 years through new tax and duty incentives that would also grant Arctic access to Russia's private players.
That announcement was quickly followed by news that Russia's second-biggest crude producer Lukoil was interested in bidding on the Arctic licenses held by its traditional state rival.
Rosneft confirmed further interest on Saturday from the Russian-British TNK-BP alliance. The firm's Russian shareholders managed to bloc BP's alliance with the Kremlin giant last year.