The winner of the award, previously known as the Samuel Johnson Prize, will receive £30,000.
It aims to recognise high quality non-fiction works published in English.
It is open to books in the areas of current affairs, history, politics, science, sport, travel, biography and the arts.
Flanders, now a chief market strategist at JP Morgan Asset Management, said: "The Samuel Johnson Prize has helped changed the way we think about non-fiction writing in this country, with a yearly reminder that great books truly can come out of anywhere - and anything.
"Personally I'm delighted to be chairing the award in its new incarnation."
Prize director Toby Mundy said: "This is the beginning of a very significant new chapter in the story of Britain's most prestigious non-fiction prize."
Submissions will be accepted from 23 May, with the winner announced on 15 November.
Former BBC Economics Editor Stephanie Flanders is to chair the judges of the 2016 Baillie Gifford Prize for Non-Fiction.