Murray, 57, who joined the club in 1988, will also resign as a board director and will be succeeded as chairman by 61-year-old Alastair Johnston, a director of the club since 2004.
"For the last 20 years I have been actively involved in the club on an almost daily basis and I think that now is the right time to take a step back," said Murray.
"I have said many times that being the chairman of Rangers is not something anyone should do forever and I have personal and business interests outside the club I would like to pursue."
"As things stand, I remain the majority shareholder at the club and will always have the best interests of Rangers at heart but it is time to pass on the chairman's baton," said Murray.
"...it is particularly gratifying to step down when the club are reigning SPL champions, Scottish Cup holders and about to embark on another exciting journey in the Champions League.
"David richly deserves his place in Rangers history as one of the club's greatest chairmen and his passion has burned brightly for 20 years," Johnston said in a statement.
