Jones will take over from Cindy Gallop, who is moving to become the chairman of the agency and the chief marketing officer, with responsibility for promoting the brand worldwide.
Jones, a BBH lifer, joined the agency in 1987 as a graduate trainee. He was promoted from managing director in April as part of the London agency's succession management programme.
BBH London will continue to be run by the chairman, Jim Carroll, the deputy chairman, Guy Murphy, and the managing director, Derek Robson, who were also promoted in the April revamp.
The announcement of Jones' move to New York coincides with the appointment of Kevin Roddy as the executive creative director in the New York office. Joe Da Silva, the operations director at BBH London, is also moving to New York as the general manager.
The management changes are aimed at boosting the New York office's US expansion. Its new-business and creative performance has not matched that of its flagship UK shop to date.
Jones will begin splitting his time between New York and London immediately. He and his family will move there for the foreseeable future in January.
Simon Sherwood, the BBH chief operating officer, said: "After six years we have a very healthy and exciting business in New York thanks to the efforts of Cindy and her team. Now is the time to add more resource and talent to the mix, giving us a broader base management team and greater strength and depth."