McMeikan has agreed to stay in the role, and remain a member of the Board, while a successor is appointed.
He joined the Board in June 2008 and became chief executive of the company in August the same year.
McMeikan was previously retail director of Sainsbury, having joined the retailer in 2005 after a short period as chief executive of Tesco in Japan. Prior to this, he had spent 14 years in operational roles within Tesco, becoming chief executive of the Europa Foods convenience store business following its acquisition in 2002.
McMeikan, said: "It has been a great honour to lead Greggs since 2008. It is a wonderful company with fantastic people and I am enormously proud of all that we have achieved together. There are many exciting growth opportunities ahead for the business and the team is well placed to deliver them.”
Derek Netherton, chairman of Greggs said he wished him well in his new role. “He has led the company through the major changes that have put us in a strong position for the future with a clear strategy for growth in a difficult environment,” he added.