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.

The Oxford English Dictionary (OED) added 19 Singaporean terms and 13 Hong Kong terms in its latest update.
"Wah" is an expression of delight or surprise, "shiok" means cool, and "yum cha" is a type of Chinese brunch.
Additions also include "blur", which means confused or ignorant, and "sabo", which means to harm or play a prank on.
The dictionary included formations of English that are mostly used in Singapore or Hong Kong.
For example, "compensated dating", a Hong Kong term, refers to the practice of teenage students providing companionship or sex in exchange for money or gifts.
And "Chinese helicopter" is a derogatory term referring to a Singaporean whose schooling was conducted in Mandarin Chinese and has limited knowledge of English.
The OED records the meaning and development of the English language.
It says that, for a word to qualify, there must be "several independent examples of the word being used, and also evidence the word has been in use for a reasonable amount of time".
Hong Kong English words:
Char siu: roast pork marinated in a sweet and savoury sauce
Dai pai dong: an open-air food stall
Kai fong: a neighbourhood association
Wet market: a market for the sale of fresh meat, fish, and produce
Singapore English words:
Ang moh: A light-skinned person, especially of Western origin or descent; a Caucasian
Hawker centre: A food market at which individual vendors sell cooked food from small stalls, with a shared seating area for customers
Chilli crab: A dish consisting of crab cooked in a sweet and spicy gravy containing red chillies and tomato
Killer litter: Objects thrown or falling from high-rise buildings, endangering people
Read more: The rise of Singlish
Former BBC Economics Editor Stephanie Flanders is to chair the judges of the 2016 Baillie Gifford Prize for Non-Fiction.
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Several Singaporean and Hong Kong English terms, including "wah", "shiok" and "yum cha", are now officially recognised as acceptable English.