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The deal, first mooted on January 8 and which will be put to shareholders at the company's next court and general meetings, is expected to complete by March 31.
Sirius' chairman Russell Scrimshaw said although recommending the deal would come as a shock to many shareholders, if approval is not forthcoming "there is a high probability that the business could be placed into administration or liquidation within weeks thereafter".
"This outcome would most likely result in shareholders losing all of their investment, as well as put the future of the entire project, and its associated benefits for the local area and the UK, at risk," said Scrimshaw.
Anglo's CEO Mark Cutifani said the offer "provides greater certainty for Sirius' shareholders, employees and wider stakeholders, while bringing the prospects for the development of this potential tier one project closer to reality".
"We intend to bring Anglo American's financial, technical and product marketing resources and capabilities to the development of the project, which of course would be expected to unlock a significant and sustained associated employment and economic stimulus for the local area," said Cutifani.