Andrews will now be responsible for setting the creative vision for the UK, ensuring it is executed across the agency's three offerings – creative, data and media.
This is an expanded remit that reflects the increasing demand for integration across all three Rapp businesses based in London.
Andrews will work across clients including Akzo Nobel (Dulux), Barclays, Barclaycard, CRUK, Google, Guide Dogs and Virgin Media.
He joins the UK executive board, which, among others, comprises the chairman, Ian Haworth; the chief executive, Marco Scognamiglio, and the managing directors of Rapp's three offerings: John Perkins (creative); Ian Maynard (media), and Colin Bradshaw (data).
Andrews said this new integrated approach to creativity "opens up a whole new world of opportunities for creative experimentation far outside the traditional boundaries".
Haslam, who was previously the most senior creative at the agency, is to become executive creative director, the top creative role, at Rapp New York. His position will not be replaced.
He replaces the husband-and-wife team Wayne and Kim Pick, who have returned to New Zealand after two years as joint ECDs of Rapp New York.