De Beers has received a £12bn takeover bid from a consortium including mining firm Anglo American and South Africa's Oppenheimer family.
The board of De Beers says it believes the transaction offers fair value for the diamond business.
It says it would also unlock the cross-shareholding structure between London-listed Anglo and De Beers.
At present, Anglo owns 32.2% of De Beers, which in turn owns 35.4% of Anglo.
A new takeover vehicle called DB Investments is behind the agreed bid of $14.40 in cash plus 0.43 Anglo American share per De Beers share.
The price represents a premium of 31% to the price of a De Beers Linked Unit of $32.90 on January 31, or a premium of 69% to the average of the daily prices of a De Beers Linked Unit of $25.57 over the 12-month period to that date.
De Beers will be wholly-owned by DBI, which will be owned by the Oppenheimer family's Central Holdings Ltd, Anglo American and the Debswana Diamond Company in proportions of 45%, 45%, and 10% respectively.
Debswana is jointly owned by the government of the Republic of Botswana and De Beers.
Anglo American intends to make a 3-for-1 bonus issue following the completion of the De Beers deal.