Murphy's departure comes after 20 years with the FT. Last year he took control of FT.com, reducing its losses by £80m after the dotcom slump.
Oliver Fleurot, managing director of the FT, said: "He is seeking new challenges outside the FT and outside Pearson. He feels it is time to seek a more entrepreneurial role."
The news comes within a few days of the announcement that Fleurot is taking responsibility of the entire FT Group after its chief executive, Steven Hill, announced that he was stepping aside to work on a possible management buy-out of FT Business, the company's magazine group.
Fleurot is aiming towards better integration of the online and newspaper sides of the FT.
The online business has been dramatically streamlined under Murphy. Online budgets were slashed last year and offshoot sites have been merged back into the main FT.com sites. There are also a number of subscription services due to be launched this summer.
A total of 150 jobs have been cut at the FT Group this year. Last year, the group negotiated the sale of all its non-financial titles, as it sought to focus on financial and business news.
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