Premier Foods is pursuing its strategy of focusing on its core brands, such as Hovis and Sharwoods.
The Elephant Atta business, a non-core brand, reported revenues of £17.8m for the year to 31 December 2011.
Elephant Atta sells a variety of flours, including medium, self-raising, white, brown and wholemeal.
Along with Primark, ABF owns food brands including Blue Dragon and Jordan. ABF's Westmill Foods subsidiary serves chefs and owners of Chinese and Indian restaurants and takeaways across Europe, in addition to its Indian, Pakistani, Bangladeshi, Chinese, African and Caribbean consumer ranges.
The disposal includes the marketing, distribution and sales of the Elephant Atta, Elephant Chakki Gold and Fassal brands on a cash and debt-free basis, while the proceeds of the transaction will be used to pay down Premier's debt.
Michael Clarke, chief executive at Premier Foods, said: "We are continuing to deliver on our growth strategies, growing our power brands, divesting selected, non-core businesses and reducing costs on track with our plans. The Elephant Atta brands are great brands that I'm sure will benefit from being part of Westmill Foods."
Premier Foods announced plans to sell its non-core assets and focus on eight key "power brands" in October last year, concentrating its efforts on growing the Hovis, Mr Kipling, Ambrosia, Sharwoods, Oxo, Bisto and Batchelors brands.