The deal will increase Anglo’s stake from its current 45pc to 75pc or 85pc, depending whether the government of Botswana exercises an option to increase its own 15pc stake. Botswana said it would consider the move in coming months.

Nicky Oppenheimer, chairman of De Beers, said the family had wrestled with the decision to sell its 40pc stake and exit De Beers but that Anglo was its “natural home”. "This has been a momentous and difficult decision as my family has been in the diamond industry for more than 100 years and part of De Beers for over 80 years," he said. "After careful and deliberate consideration of the offer, and what is in the best interests of the family, we unanimously agreed to accept Anglo American's offer."

The deal was seen as signalling Anglo’s bullish outlook on diamond prices. Demand for diamond jewellery is growing in booming emerging markets but supply is tight, with new discoveries lacking.

Cynthia Carroll, Anglo’s chief executive, said in a statement that Anglo’s scale, financial power and technical skills would allow De Beers to “capture the potential presented by a rapidly evolving diamond market".

Analysts suspected succession issues were behind the sale, coming after years in which the Oppenheimers have resisted Anglo's approaches. “Nicky Oppenheimer is 65 and there is no obvious family member coming through the ranks to take managerial control,” said Dominic O’Kane at Liberum Capital.

There was speculation that a float of the diamond company could be on cards, given that under the agreement Anglo must pay extra to the Oppenheimers if De Beers goes public in the next two years.

Analysts were divided over whether the price was good value. Nick Hatch at Royal Bank of Scotland argued that Anglo's roughly $1bn overpayment for the stake, based on his calculations, looked large even accounting for a “control premium”.

The fortunes of the Oppenheimers and Anglo have always been intertwined. Sir Ernest Oppenheimer, who founded Anglo in 1917, took control of De Beers in the 1920s. The Oppenheimer family still own around 2pc of Anglo and until Nicky Oppenheimer stepped dowm this year a member of the family has always sat on its board. The sale is expected to close in the second half of next year.