Lafarge India operates three cement plants and two grinding stations with capacity of about 11 million tonnes a year.
"LafargeHolcim announces it has entered into a letter agreement with Nirma Ltd... For the divestment of its interest in Lafarge India for an enterprise value of approximately USD 1.4 billion," the company said in a statement.
Lafarge India also markets aggregates and is one of the country's leading ready-mix concrete manufacturers.
"The proceeds from the divestment will be used to reduce debt further," the statement said.
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"This agreement is an important step in our 3.5 billion Swiss franc (USD 3.56 billion) divestment programme.
"With this deal, two thirds of the programme have been secured and the remainder is well on track. We are confident that we will meet our target by the end of this year. With the proposed buyer we have found the right partner who will be able to develop the business further in the interest of all our stakeholders," CEO Eric Olsen said.
LafargeHolcim has a divestment target of 3.5 billion Swiss franc in 2016 and has already completed the sale of its business in South Korea and signed an agreement to divest its minority shareholding in Saudi Arabia.
The Group has also expanded its joint-venture with SNI, its historical partner in Morocco, by merging Lafarge Ciments Maroc and Holcim Maroc to create LafargeHolcim Maroc.