Carolyn McCall, who is moving to easyJet, will step down as chief executive at the end of June.
GMG says the company is in the process of appointing executive search consultants and will consider both internal and external candidates.
The recruitment process will be led by a nominations sub-committee chaired by Amelia Fawcett, chair of GMG, and includes Liz Forgan, chair of the Scott Trust, and non-executive directors John Bartle and Neil Berkett.
Miller was appointed to his current role in August 2009. Prior to that he was group chief financial officer of Trader Media Group, publisher of Auto Trader, which is jointly owned by GMG and Apax Partners for more than six years.
Earlier this week, Guardian News & Media (GNM) appointed former Absolute radio brand chief Chris Lawson to the new role of content sales and marketing director http://www.marketingweek.co.uk/news/guardian-appoints-former-absolute-brand-boss-as-marketing-chief/3012475.article.