The former Asda chief executive is Royal Mail's longest-serving chairman, having taken the position in March 2002 after joining as a non-executive director in 2001.
Leighton's departure will break up his long-running double act with chief executive Adam Crozier, who joined in February 2003.
The pair have led the company through a restructuring process that took it from losing £1m per day to making a substantial profit, though its finances have since weakened.
The powerful Communication Workers Unions has frequently clashed with the pair over issues such as the potential privatisation of the company, and embarked on extensive strike action last autumn in protest at changes to pension benefits.
The debate over Royal Mail's ownership structure and future is likely to be stirred again by the publication of the Hooper Report on the future of the postal services market next month.
The Department for Business Enterprise and Regulatory Reform has engaged headhunter Zygos Partnership to lead the search for a successor.
Last year the Government extended Leighton's term after making a number of unsuccessful approaches to businessmen, including Sainsbury's chairman Sir Philip Hammond, to succeed him.
Crozier said: "Allan is the longest serving chairman of the company and his leadership has seen the company take huge steps forward. He remains chairman for a further six months and I know he will continue to lead the company with the enthusiasm, passion and drive that is his hallmark until he steps down."