Lawson, who will also retain the group managing director role, will continue to report to Edwards.
The promotions follow growth at the UK group, which also includes the relationship marketing arm, Arc UK; the experiential business, Lime; the brand activation arm, LeoSports; and the luxury division, Atelier. Edwards and Lawson were appointed to their group roles three years ago. Leo Burnett is now exploring how it might expand further in the UK and is considering acquisitions.
Lawson becomes the chief executive seven years after joining the agency as the group communications director in charge of McDonald's. He previously worked at Grey London, Lowe Howard-Spink and WCRS.
The promotions follow the appointment last November of Justin Tindall, previously the creative partner at The Red Brick Road, as Leo Burnett's executive creative director.
Edwards said: "Paul's promotion is a well-deserved recognition of the fact that he has been wearing two hats for some time now: the first as my deputy when it comes to broader group responsibilities, the second as leader of the group's advertising practice."