Nottingham-born Fletcher, 41, began his broadcasting career in the city.
Sports PR firm founder Paul Mace, a lifelong Magpies fan, and property consultancy director Jon Enever have also joined the club.
Chief executive Jason Turner becomes football operations director, with Corrine Rigby as finance director and Amanda Fletcher as commercial director.
Chairman Alan Hardy said: "I am delighted to have put together such a strong team of people who have a diverse and complementary range of football and business skill sets.
"Football is a team game and it is important that we have a committed, enthusiastic and experienced senior group in place dedicated to getting Notts County back to where they belong in the English footballing pyramid."
Enever is a board member of Nottingham Means Business and chairman of Talented Enterprising Nottingham, while Mace wrote the 250,000-word Notts book One Flew Over The Magpies Nest.
Turner arrived at Meadow Lane in April 2016 after previously holding similar positions with Newport County, Plymouth and Cardiff City, while Rigby and Fletcher were both executive appointments by Hardy when he took over the club in January.
BBC Radio 5 live presenter Darren Fletcher is one of six appointments to Notts County's new board of directors.