The announcement came just four days before Rangers set off for Florida to set up a winter training camp.
Brannan, who leaves Ibrox after just six months having previously been the manager at a whisky company, gave his reasons in a statement released by the club.
"I have today resigned my position as director and chief executive of Rangers," he said. "I took the decision more than a month ago that I did not want to follow a long-term career in football. In recent weeks I have been pursuing other career opportunities and felt it appropriate to make my intentions known to David Murray [the Rangers chairman] given the high- profile nature of my position.
"I would like to thank David for the opportunity he has given me to work in football and regret the timing of my decision. I wish the club every success for this season and beyond. This concludes my statement and I have no intention of commenting further either now or in the future."
Murray will now take charge of day-to-day operations at the Scottish Premier League leaders. "I am disappointed for both parties that it didn't work out. I personally wish Bob well in his future career," Murray said.
"I will assume responsibility for day to day operations at the club. There will be no further statement on this issue."Reuse content