Roger Whiteside, who ran Marks & Spencer’s food arm before becoming a founding managing director of online grocer Ocado, has been a non-executive director of Greggs for four years.
He also led a turnaround of off-licence group Threshers. Whiteside will take over from McMeikan, who quit in December to take up the chief executive role at catering firm Brakes Group, on 4 February.
Greggs chairman Derek Netherton said that Whiteside, 54, had helped develop the group’s strategy of rapid expansion in recent years.
He added: “He is very well respected within the company and his appointment will enable a smooth transition in what is still a challenging consumer environment.”
Punch, whose 400 pubs in Scotland include Edinburgh’s Malt Shovel, is not currently looking for a new chief executive.
Punch said non-executive chairman Stephen Billingham will become executive chairman.
Whiteside, who it is thought will get a similar salary to McMeikan – £470,000 in 2012 – said: “Greggs is a great business with an iconic brand that has strengthened considerably over the past few years. I believe we have a great future.”
Greggs posted a near-3 per cent fall in festive sales recently, blaming wet weather and fewer shopping hours.