Adam Arnold, the BBH deputy chairman and chief executive of BBH’s branding arm Zag, will take over Exon's role at BBH.
After 19 years at BBH, the last two as MD, Exon will lead the London, New York and LA Sunshine offices. Kit Hawkins, a founder of Sunshine, becomes executive chairman, with a brief to drive the North American business and the company's Entertainment division.
Hawkins said the agency is tracking to double its size in terms of revenue this year and that Exon's expertise in running a creative company would bolster the management line-up. Exon will be given equity in the company without having to buy-in.
She has become the third senior member of staff to quit BBH in the past month, after it was announced that both the joint chief strategy officers Jonathan Bottomley and Jason Gonsalves were leaving.
Bottomley is moving to New York and Gonsalves is taking the CEO role at McGarrybowen. In an email to staff, BBH chief executive Ben Fennell said Exon had been "a moderniser, an innovator and a force for positive change".
Adam Arnold started his career as a graduate trainee at BBH in 2000, working on accounts such as Audi, ITV and Vodafone before moving to Zag in 2006.
Fennell said: "We continue to take great pride in promoting from within and I couldn’t think of a better leader than Adam to take BBH forward.
"Adam leads with the hunger and energy of the many startups he's worked with. He is creative, commercial and fiercely proud of BBH. ‘To zag’ is not just a set of words for Adam, it is a belief system. He will connect our past with our future."