Dame Suzi is chair of the Charity Commission and was formerly deputy chair of the FSA and chair of the School Food Trust.
The council will advise Hilary Benn, secretary of state for environment, food and rural affairs, on food affordability, security of supply and the environmental impact of food production.
Defra is inviting applications from other potential members.
The Food and Drink Federation said it was important that individuals with industry experience were on the council.
A Defra spokesman said the council was unlikely to have met in time to influence a statement of policy on food security and supply, expected by the end of the year, but would be able to influence future policy.