Craig, 46, currently general manager of ABP Scotland, will take over from ANM's CEO Brian Pack, who is due to retire at the end of April.
Having spent all his working life in the meat industry, Craig started out as an apprentice butcher on leaving school.
John McIntosh, chairman of ANM Group, said that the board were delighted to have recruited someone of Alan's ability, energy and experience to lead the Group forward
He said: "We had an excellent field of candidates from which to choose after an exhaustive search of the UK and beyond. However, Alan stood out as a natural leader with vision and a proven track record in an area central to the group and first hand experience of livestock auctions and farmer procurement groups as a customer.
"I have no doubt that the group's excellent staff and management team will enjoy working with Alan to take the group forward in these challenging times."
Craig added: "I am really looking forward to getting started and developing a full understanding of the group in all its aspects and building on its strong financial base and excellent staff. I fully appreciate the importance of the group to the Scottish agricultural industry and look forward to playing my part."
Craig also takes over as president of the Scottish Meat Wholesalers in April.