The news comes less than a week after Peter Beadle left his position as the National League North club’s manager.
Harris, who stepped down at Tamworth recently, is now looking to recruit a head coach.
Hereford announced they are going in a new direction in an attempt to take the club into the Football League.
Harris told the club’s website: “I am absolutely delighted to have been given this opportunity.
“My father and my uncle were big Hereford United fans and they took me many years ago.
“I will give everything to help this great club progress to where it deserves to be.”
Chairman Ken Kinnersley thinks it’s the perfect appointment.
“We are delighted Tim has accepted the position and we feel he is a perfect fit in the new structure,” he said.
“He impressed every member of the board greatly when we met him but most of all he has great experience.
“We very much look forward to working with him.”