McCracken spent seven years as chairman of Duchy Originals before joining The Co-op Group and prior to that held senior roles at M&S for nearly three decades, including director of the food division from 1993 to 1998 and joint MD from 1994 to 2000.
He is also a member of the Defra Council of Food Policy Advisors. "I am delighted to be joining Branston, which is widely respected for its leadership in the industry," he said.
McCracken's experience would take Branston into a "further important period of development", said MD Graeme Beattie. "He has fantastic experience in the fresh food industry, which will add a real retail focus to our business," he said.
"Now that Branston has become a leading retail supplier, our company has a change of emphasis and focus and Guy will be able to offer his huge knowledge of the food sector."
Departing chairman Howard will remain a major shareholder. He has been with the company since its formation in the 1960s and was a key figure in winning the Tesco account in 1990.
Branston is Tesco's biggest potato supplier and its turnover has risen from just £5m in 1998 to £110m today.