Greggs said today that he will stay on in his role until a successor is appointed. It has begun a search for a replacement.
McMeikan was appointed chief executive of Greggs in June 2008.
He was previously retail director of Sainsbury's. He has also served as chief executive of Tesco in Japan, and spent a total of 14 years at Tesco.
Greggs, which has 1,600 shops in the UK, reported that its like-for-like sales had dropped 2.6% in the 14 weeks to October 6, blaming rising food prices and adverse weather conditions.
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