The departure comes three weeks after the agency rebranded as part of parent Cordiant's FD International network of financial communications firms, which are headed by CEO Charles Watson.
FD confirmed it was not planning to replace Jones.
FD Morgen-Walke will undergo a management reshuffle, with senior MD Doug Sherk becoming CEO (West Coast), and MD Anton Nicholas rising to senior MD and chief operating officer (East Coast).
Jones's departure nearly completes an exodus of the firm's top-brass that began shortly after Morgen-Walke was acquired by UK-based Cordiant in 2000, when Cordiant bought Morgen-Walke's former parent Lighthouse Global. After the acquisition, the firm's founders, Lynn Morgen and David Walke, left, followed by four MDs.