FSA chief executive Hector Sants says Murray will leave the role in December.
Murray was appointed in April 2006 to head up departments handling strategic communications, media relations, public affairs, internal communications and events and conferences.
He joined the FSA from Powerscourt, a financial public relations firm he co-founded with former Sunday Times business editor Rory Godson.
Murray started his career in journalism during which time he held positions as business news editor of the Independent, city editor of both the Daily and Sunday Express and executive editor of the Daily Express.
In an internal communication to staff, seen by Money Marketing, FSA chief executive Hector Sants said: “John informed me earlier this year that he wished to move on after almost four years at the FSA. In that time, he has made a vital contribution to guiding the organisation through some of the most trying circumstances any of us have ever seen. We agreed he would stay until the end of the year and then take three months’ garden leave before moving on to fresh challenges.
“John has transformed the communications function during a period when the spotlight on the FSA has been at its most intense. I am personally very grateful for his support and the quality of his advice throughout the financial crisis and beyond.”