The former HHCL creative chief replaces Jim Thornton, who left in July this year.
Burley, who joined Burnett last year as a creative director, will take overall control of Leo Burnett's 40-strong creative department, and will run the agency alongside Paul Lawson, the managing director, Ali Bucknall, the planning director and Nina Jasinski, the marketing director.
However, the agency is still on the hunt for a creative director to work alongside Bruce Haines, the group chief executive, and oversee the creative strategy of the whole Leo Burnett group, including Arc, its direct marketing shop.
Burley said: "I am going to inject more ambition into every department."
Jim Bolton, Burley's creative partner, will work with him on creative duties and help to run the creative department.