Allen takes over from Patrick Bergin, whose appointment as chief operating officer was announced in November 2016.
Allen, who takes up the post on February had several roles at British American Tobacco, most recently regional finance controller for the European, Africa and Middle East regions.
William Rucker, Crest’s chairman, said: “We are delighted to be welcoming Robert onto our board and are confident that he will make a significant contribution in helping to deliver the growth ambitions of the business.”
Chris Tinker, a member of the group’s executive management team, also joins the board, becoming chairman of major projects and strategic partnerships.