Vickers takes over from Dave Matthews, who becomes chief financial officer.
"We are now reaching the point where we need to expand the back-office operation, having completely rejuvenated the playing side of the club," Vickers told reporters.
"It is a great privilege to head up this club as it forges its new path into Super League.
"The rugby league world is closely scrutinising everything that Marwan Koukash is doing here. It is exciting times and we are determined to be in the best possible shape for the kickoff."
Salford's backroom reorganisation is part of owner Koukash's ambitious plans to turn the club that finished bottom in the Super League last season into potential champions.