The news will be a major disappointment to thousands of Yorkshire investors, who bought into the company thinking they would make a big profit.
However, Anglo American said its intention is to create a significantly higher number of permanent jobs, which will be welcomed by many in the area.
The offer is for 5.5p per Sirius share. While this is a premium of 34 per cent to the closing price of 4.1p on Tuesday, it is way below Sirius' previous share price. An investor who put £100 into Sirius a year ago would have only £18.60 worth of Sirius shares at the last close on Tuesday.
Almost half of the company’s shares are held by 85,000 small investors, including 25,000 shareholders in Yorkshire and the North East. Around 10,000 investors live in the immediate region of the mine.
Many of them took to Twitter to vent their anger at Sirius' management.
One investor called Chris said:"Seems you have no thoughts for the 85,000 odd shareholders who trusted your company with their life savings, selling out at such a cheap price is frankly ridiculous, surely you can explore other options otherwise ordinary folk lose out and never get their money back."
He added that he would make "an eye watering loss" on his investment, adding: "In short we will be shafted".
Another investor called Landore said: "They don't give a rat a*se about shareholders."
Anglo American expressed sympathy for small shareholders, but said the project requires significant further capital.
The firm's finance director Stephen Pearce told the Yorkshire Post: "We do appreciate that different people will have come in and invested in Sirius at different levels and obviously we have some sympathy for those people who perhaps invested at higher values.
"We think it's a fair value for where the project is today and given the capital expenditure that still has to be spent on the project.
"We are focused on the broader benefits this brings to the region. I think the Sirius team have done a terrific job in terms of the relationships they have established with the local communities, councils, national parks. We really look to build on those relationships that they have worked very hard to establish over recent years."
He added that North Yorkshire is a region with a proud mining heritage and Anglo American is keen to develop this.
The offer comes after a tough few months for Sirius, which was forced to go back to the drawing board in September when it failed to raise enough money to unlock the bank loans it needed to push ahead with its fertiliser project.
The business hoped that a bond sale would allow it to borrow up to £1.9bn from banks.It was forced to slow down work on the mine in North Yorkshire after the announcement, and later came back to the market with a slimmed-down plan for how to progress.
The plan for the mine involves tunnelling under North York Moors National Park to exploit what Sirius has said is the world’s largest deposit of polyhalite, a multi-nutrient fertiliser.
Mr Pearce said: "For Sirius shareholders, this possible offer could provide certainty whilst the prospect of Anglo American's financial, technical and marketing resources should help progress the project over time.
"This would be in the interest of Sirius' broader stakeholders including employees and customers, as well as the prospect of broader benefits for the local area from the project."
When asked what guarantees he could give on jobs, Mr Pearce said: "Our intention is absolutely to continue to develop this project. That's why we think it adds great value to us as an organisation and to the region.
"What you will see as the project moves from the construction phase to the operating phase is the establishment of far more significant permanent jobs than the current situation in the development phase.
"We are quite excited by the opportunities that the project brings to the region and the employment that will follow."