He will report to Richard Pinder, Publicis Worldwide's chief operating officer. Pinder becomes the chief executive of the UK group of companies, including Dialog and Modem, as part of the move.
Simpson joins later this month and will work with Nik Studzinski, the executive creative director, and Kym Douglas, the executive planning director. Publicis has been without a leader since Grant Duncan, the previous UK chief executive, left in March. Tim Lindsay, the UK group chairman, left two months later.
Pinder said: "Neil's experience on both sides of the fence and his eye for good creative are just what the agency needs."
Simpson added: "There is no reason why we can't be the most creative of the multinational agencies in London."
Simpson began his career at Ogilvy & Mather. He joined Coca-Cola in 1993 as the European ad director before moving to Adidas as a senior vice-president. In 2002, he became the global marketing communications director for Vodafone. He left in 2006 to set up his own business.