Manager Ally McCoist confirmed last week that his former Ibrox team-mate had been suspended.
And a club statement on Tuesday evening read: "Rangers' chief scout has been in talks with the club for more than a week and both Rangers and Neil have agreed to part company."
Rangers refused to expand on the reasons for Murray's departure but insisted it was not because of any "scandal".
The statement added: "This club has neither suggested nor said anything of the kind. In fact, Rangers are happy to point out that Neil has agreed to act as a consultant for the club."
Rangers added that they were embarking on a "far-reaching restructuring programme at various levels of the club".
The statement, which hit out at reporting of Murray's suspension, finished: "Rangers and Rangers fans will stand together. And together we will return to the top."
McCoist confirmed on Friday that the club had launched a probe regarding Murray and urged the situation to be resolved quickly as Rangers embark on more rebuilding work in the summer in time for the end of their transfer embargo on September 1.
McCoist, speaking a day before his team clinched the Irn-Bru Third Division title, said: "Neil has been suspended by the club pending an investigation. It's a really sensitive matter and that's all I can say on it."
Murray, who played for Rangers during the 1990s, was appointed to the role in 2011.
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