Fox is president of the new board, which has its first meeting in Bristol today.
The aim of the board is to increase inclusion and benefit from free trade across the UK and it holds representatives from Scotland, Wales and Northern Island.
Board advisers include Collette Roche, chief of staff at Manchester Airport, former president of the Board of Trade Patricia Hewitt and Ian Curle, CEO of the Edrington Group, which produces The Famous Grouse whisky.
“The advisers on the board will act as the ‘eyes and ears’ of the modern businesses community to ensure the benefits of free trade are spread equally across the country,” Fox said.
The board will meet four times a year and will be rotated around the UK to ensure each part of the union is represented.