Both men joined the board of the Rangers International Football Club - Murray as chairman and Cartmell as a non-executive director - under the stewardship of former chief executive Charles Green.
Murray stepped down from his position in May amid speculation over his future with the club but had remained on the board as a non-executive director.
In a statement, Ibrox non-executive chairman Walter Smith said: "Both Malcolm and Phil have made important and valuable contributions to the club.
"The last year has presented the club with a number of challenges and it has been beneficial to have two highly experienced non-executive directors such as Malcolm and Phil offering assistance.
"On behalf of the board I would like to thank them for their considerable efforts in helping to rebuild Rangers.
"Both men have other significant business interests and we wish them well in their future endeavours."
Following the duo's departures, Rangers announced that businessman James Easdale bad been appointed to the club's board as a non-executive director.
The 42-year-old is a director in a number of businesses including McGill's Bus Service Limited, an indepenent bus operator in Scotland.
In a statement to the Stock Exchange, Easdale said: "As a lifelong Rangers supporter, I am proud and honoured to serve on the board of such a great sporting institution.
"I look forward to helping Rangers Football Club continue its journey back to the top of Scottish football."