Ineos, which is controlled by billionaire chairman Jim Ratcliffe, said the move will propel it into a top ten company and the biggest private group operating in the North Sea.
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It will boost its so-called upstream division, seeing it add a portfolio of production, development and exploration sites off the coast of Denmark, Norway and West of Shetland area.
Around 440 staff will also transfer from Dong on completion of the deal, which is expected in the third quarter.
Ratcliffe said the business was a “natural fit” for the group as it expands its upstream arm.
He added: “This business is very important to us at this stage of our growth plans and we are delighted with the expertise that comes with it.”
Ineos has agreed to pay $1.05bn and a further potential $250 million for the Dong division.
Henrik Poulsen, chief executive of Dong, said: “Since the decision in 2016 to divest our upstream oil and gas business, we’ve actively worked to get the best transaction by selling the business as a whole, getting a good and fair price for it and ensuring the optimal conditions for the long-term development of the oil and gas business.
“With the agreement with Ineos we’ve obtained just that.”
The acquisition comes after Ineos recently snapped up a 235-mile pipeline from BP, which transports nearly 40 per cent of the UK North Sea’s oil and gas production, for up to $250m.
Ineos employs around 18,500 people across 105 sites in 22 countries. It is the 200th largest business in the world, with sales of $40bn a year.
When it launched in 1998, the group had 400 staff and annual sales of $200m.