The tobacco company announced it had promoted Gray, previously regional director EEMEA, to the role. He takes up the position on Monday.
Gray has been on the board for seven years and has been with the company for a total of 27 years in various senior management positions.
Levy, who has been with the group for 21 years and had been marketing director since 2009, has been appointed special projects director in the interim, before he steps down from the board on 31 December.
The group announced that Johan Vandermeulen, currently general manager for BAT Russia, will succeed Gray. Tadue Marroco, currently head of strategy and planning and M&A, has also been promoted to the board in the role of business development director, effective from1 September.
Chief executive Nicandro Durante said: "We will all miss Jean-Marc’s abundant energy, passion for the consumer, inspiring leadership and his unstinting commitment to the business. He leaves a very significant legacy. I would like to thank him for all that he has done for the organization.
"I am pleased about Andrew’s appointment as group marketing director, where he will bring his keen commercial acumen and significant group-wide experience to bear."