"Under the terms of the agreement Statoil will, subject to the approval of the Greenland government, acquire a working interest of 30.625 percent in the Pitu licence," Cairn said in a statement.
"Cairn will retain operatorship (56.875-percent interest in the block) of the exploration and Statoil will operate any future development. Nunaoil has an ongoing 12.5 percent interest in the block."
Edinburgh-based Cairn, whose fortunes were transformed in recent years by successful exploration projects in India, has since turned its focus to offshore Greenland.
However, two drilling campaigns failed to locate commercial quantities of oil and gas in 2010 and 2011.
"Statoil's extensive Arctic operating and development experience makes them the partner of choice for the Pitu block where we see significant potential," Cairn chief executive Simon Thomson said on Monday.
Cairn last month finalised a deal to sell a controlling stake in its Indian unit to mining giant Vedanta, after protracted wrangling over royalty payments.
"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," Thomson added in Monday's statement.