The intention is to move to 58% Vedanta ownership, while Cairn Energy reduces to 22%.
The acquisition will be covered by a combination of about 43% cash and 57% Cairn shares.
Cairn's share price rose by more than 5% in early trading following the announcement.
Cairn recently opened a small office in Madrid and is currently pursuing other acreage in Spain.
Edinburgh oil and gas explorer Cairn Energy has announced a fresh deal in Senegal.
Esperanza, confronted a Danish warship that has been patrolling a 500-meter exclusion zone around Cairn's wells.
Shares in Cairn fell by about 6% early on Tuesday after the update was released.
Greenpeace has previously occupied vessels operated by Shell and Cairn Energy over the issue.
BBC: Greenpeace activists board Russian Gazprom oil platform
I've written before about the problems Cairn Energy had in exiting its Indian investment.
Last year, Cairn sold most of its stake in the highly successful Indian operations.
Cairn had estimated that the Skarfjell discovery contained between 60 million and 160 million barrels of oil.
Cairn however said it was still "committed to Greenland" and was "excited about the potential of the region".
The move came as 17 activists appeared in court in connection with the protest at Cairn's offices in Edinburgh.
Cairn has a 20% interest in Skarfjell, which is operated by Wintershall Norge.
Cairn said it would pay 450 pence for each Nautical share, representing a 51% premium to Nautical's closing price.
The "completion of this transaction...represents a major milestone in Cairn's history, " Simon Thomson, chief executive of Cairn Energy said.
The B974 Banchory to Fettercairn road at Cairn O'Mount and the B976 Crathie to Gairnshiel road were also closed.
"Cairn India's Rajasthan asset is world class in terms of scale and cost, delivering strong and growing cash flow".
The interim interdict, granted by the Court of Session, also prohibits any attempt to disrupt Cairn Energy's lawful business operations.
Cairn Energy has insisted its operations comply fully with some of the most stringent safety regulations anywhere in the world.
If the sale of a further 30% stake in Cairn India goes ahead, the same lower share valuation will hold.
But GPI gave no such undertaking, prompting Cairn to seek a permanent interdict against GPI at the Court of Session.
Sites include Sithean Dubh, a chambered cairn where in 1831 it was said two skeletons of "gigantic size" were found.
In a statement, Cairn said it noted that court enforceable undertakings were agreed by Greenpeace UK and Greenpeace Limited in 2011.
Cairn says it has found natural gas in thin sandlayers in one of its test wells, indicating the presence of oil.
Shares in the Edinburgh-based oil exploration firm Cairn Energy fell on Tuesday on negative news over its drilling operations in Greenland.
Cairn Energy is to focus its drilling efforts in 2013 in the North Sea, and off the Atlantic coast of Morocco.
The occupation came only a few weeks after Cairn announced it had begun drilling at two wells off the coast of Greenland.
Cairn Energy has won a court order preventing Greenpeace from publishing any material recorded by protesters who occupied its headquarters on Monday.
Cairn Energy will now be able to focus on drilling in Greenland, where it has yet to find commercial quantities of petroleum.
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