Lafarge Tarmac was formed in January 2013 following the merger of Anglo American and Lafarge's cement, aggregates, ready-mixed concrete, asphalt and asphalt surfacing operations in the UK.
France's Lafarge, which entered the UK market in 1987 and acquired Redland in 1997 and Blue Circle in 2001, is planning the sale of the operation in order to secure regulatory clearance for its merger with Switzerland's Holcim, which owns Aggregate Industries in the UK.
As a result of the Lafarge Tarmac sale plan, Anglo American will sell its stake in the UK business to the French company for at least £885 million, although this is subject to the Holcim merger getting the go ahead.
Anglo, headed by chief executive Mark Cutifani, had previously planned to pursue a stock market listing of the business within two years of completing the joint venture agreement.
It said it will use the proceeds from the deal to pay down debt.
Lafarge Tarmac, which employs 6,600 staff at 330 sites with more than 30 of those in Scotland, produces 45 million tonnes of aggregates and seven million tonnes of asphalt a year.
It has more than 70 production plants and more than100 quarries nationwide.
The merger of Lafarge and Holcim is expected to be completed in the first half of next year. Both sides say they hope to have a definitive agreement in place in the third quarter of this year.
As well as Lafarge Tarmac, the two companies have announced plans for a number of other asset disposals across Europe.
"The deal is in line with Anglo's stated strategy to consolidate its operations and focus on core divisions," Citi analysts said in a note to clients.
"Though the deal value is just 4.1 per cent of the company's current market capitalisation, we believe it will provide much needed support to Anglo's balance sheet."