Jones joined the agency as its first graduate trainee in 1987.
The move also sees BBH name a new management tier; Derek Robson becomes the agency's managing director, Guy Murphy moves to the position of deputy chairman and Charlie Rudd takes the deputy managing director role.
Nigel Bogle, BBH Group's chief executive, said: "This is about putting deeper management resource against a growing business, so we don't overstretch. It will not be much of a culture shock for anyone. The three people concerned have more than 30 years at BBH between them and everyone here knows how good they are."
The London management team will report to the chief operating officer, Simon Sherwood.
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