The numerous changes to the hierarchy are a result of the club accepting an emergency loan offer from Newcastle United owner Mike Ashley, who recently increased his stake in the club to 9%.
Reports have claimed that part of the loan offer's conditions from Ashley included the removal of both Nash and Wallace.
A statement from Rangers on their official website said: "The directors would like to thank Graham for his contribution to the club during a difficult period. The board has commenced the search for a chief executive officer. A further announcement will be made in due course."
The Scottish outfit have also confirmed that they have entered a "credit facility agreement" with MASH Holdings Limited, which is owned by Ashley and will provide an interest-free loan of £2m for six months.
The agreement also allows Ashley's company to appoint two directors and widespread reports have claimed that Derek Llambias will be added to the board.