The founding Jordans family retains control of the business, which is based at Biggleswade, Bedfordshire. It had sales of £81m for the year ended February 2007 and gross assets of £40m.
In a statement, the Jordans family said they had been looking for a long-term partner for the business and already work closely with ABF companies.
ABF chief executive George Weston said: “Jordans is a wonderful brand which is positioned well to benefit from the consumer’s growing desire for natural ingredients and healthy eating. I look forward to the development of the brand’s full potential.”