Deal will see Cairn and Statoil also share exploration costs in the Pitu region nort west of Greenland
The deal following an unsuccessful $600 million (s385 million)drilling campaign last year.
Under the terms of the new agreement, Statoil will take a 30.6 per cent stake in Cairn's Pitu Licence located in seas known as iceberg alley north west of Greenland.
The financial details of the deal have not been disclosed, though Statoil will pay an up-front payment to Cairn and will meet other costs.
Cairn said at the conclusion of its 2011 Greenland drilling programme it remained committed to exploration in the region but was considering a joint venture partner to share the risks of further drilling in the 102,000 square kilometres it has authority to explore.
The Edinburgh-based exploration firm spent $400 million (s256 million) on its failed 2010 exploration programme offshore Greenland.
However, Cairn currently has a cash balance of $4.7 billion (s3.02 million) following the completion last December of its sale of a 40 per cent stake in Cairn India to Vedanta Resources.
Cairn chief executive Simon Thomson said: "With a strong balance sheet and the first Greenland farm out completed, Cairn is well positioned to access new opportunities and further growth in 2012.
"The completion of the transaction with Vedanta crystallises the very significant value creation that we have delivered from the Indian business allowing us to return $4.5 billion to shareholders over the last five years.
"In Greenland, Statoil's extensive Arctic operating and development experience makes them the partner of choice for the Pitu block where we see significant potential."
Cairn believes reservoirs in the Greenland region may contain more than 3.2 billion barrels of oil though industry analysts believe the total potential reserves could be far higher.
Energy consultancy Wood Mackenzie estimates Greenland could have reserves of 20 billion barrels of oil.
Exxon Mobil, Royal Dutch Shell and Husky Energy are also planning to explore in the Arctic region offshore Greenland.
Last week it was reported Cairn was considering buying either a stake in Rockhopper Exploration's acreage in the contested Falklands region or buying Rockhopper outright.