Jeff, who will leave the day-to-day running of the team to head coach Glen Pennyfather and relinquishes his manager's role immediately, will oversee the whole of the club's footballing side from the juniors through to the first team.
City will not be filling the manager's role with Pennyfather taking charge of team selection and tactics.
Club chairman Mansell Wallace said today: "The changes are with immediate effect and we're glad to have Jeff joins us on the board.
"The manager's position will not be filled but Glen will be in charge of team affairs and of course Jeff will be on hand to liaise and help him," said Wallace.
"This is all part of continuing to build the club for the long term future and obviously we are looking to gain promotion to the Conference Premier next season and believe this new set up will further help," he said.
King said: "I'm delighted to be joining the board in becoming director of football at the club and really looking forward to next season already."