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While the all-stock transaction was valued at $US2.1 billion, Noble also said it would take on Rosetta's net debt of $1.8 billion.
The deal gives Noble, which has faced considerable challenges in advancing the giant Leviathan find in offshore Israel, entry into the Eagle Ford and Permian shale oil plays.
"The Eagle Ford and the Permian are premier unconventional resource plays, two of the most economic in the US, which will expand our resource base and development inventory and further diversify our portfolio," Noble president, chairman and CEO Dave Stover said.
While Royal Dutch Shell kicked off the petroleum industry's mergers and acquisition season last month with its $70 billion friendly takeover offer for BG Group, Statoil and Aramco are have joined a growing list of potential predators.
Norwegian giant Statoil has made a series of project cutbacks and delays during the underway downturn but is also keeping an eye out for any bargains.
"Acquiring barrels might be cheaper than exploring for barrels, so we are monitoring it very closely," Statoil chief financial officer Torgrim Reitan said according to Bloomberg.
"There are a lot of assets for sale. But I think it's fair to say that high-quality assets are still not cheap."
Meanwhile, three sources told the newswire that Aramco is budgeting to spend between $70 billion and $80 billion on overseas acquisitions and investments during the next five years.
"The investment is part of the state-owned company's target of spending $150 billion at home and internationally through 2019, the people said, asking not to be identified as the information is private," the newswire claimed.
Aramco's acquisition hunt will focus on Asia and especially China and Korea.