South African-born Stewart was previously chief executive at Thomas Cook UK, where he helped the business through tough times by implementing a rigorous restructuring programme. He left Thomas Cook two years ago.
WHSmith's incumbent group finance director John Warren steps down from the business today. Warren, who has left by mutual agreement, said the sale of the international businesses has left him with a reduced role.
WHSmith group chief executive Kate Swann said: 'I am delighted to welcome Alan to WHSmith. He is an experienced finance director with strong operational skills and a solid track record of turning around an underperforming business.'