She will replace Camilla Tappin, who left the agency in August to take up the same role at M&C Saatchi.
While at Wunderman, Holme helped the agency win new business with Rolls-Royce and Scottish Courage.
Paul Lawson, the managing director of Leo Burnett, said: "Her experience in both direct marketing and creative agencies is the perfect combination for us. New-business pitches are looking for the big idea. Laura will give us this."
Holme started at The Bastable Hazlitt Partnership in 1988 as an account manager. In 1997, she joined CDP as an account director before taking up the new-business director role. She worked there until 2001, when she set up her own company, The Consultancy Group, where she worked with agencies such as Abbott Mead Vickers BBDO and InterRealtions. She moved to Harrison Troughton Wunderman in 2003.