He will replace Roy Frodsham who is moving to become managing director of Star News Shops - the independent retailer that Midcounties is going to acquire on 3 March.
Cresswell will take overall responsibility for the operation and direction of the society's 148 supermarkets and convenience stores.
His main objectives would be the continued development of the society's food retail business and delivering the best in modern, local and urban retailing, he said.
"A real attraction for me in this post is the co-op's support for the local community within the framework of co-operative values," he said.
"I am confident this approach will ensure that we strengthen our claim to be the community retailer and will lead to our continuing success."
Midcounties' chief exec Ben Reid said he had "no doubt" Cresswell had the necessary qualities to ensure continued success of food retail at the co-op.
"Andy has already made a significant contribution to our food group since joining as retail operations manager in 2002, and I am confident he will bring his undoubted drive and enthusiasm to this senior role," said Reid
The Midcounties Co-operative, formed in September 2005 with the merger of Oxford, Swindon & Gloucester and West Midlands Co-ops, trades in Gloucestershire, Wiltshire, Shropshire and Worcestershire and the surrounding counties.
It is the fourth-largest Co-operative society in the UK, with an annual turnover of £0.5bn. It has 460 outlets and 7,000 employees. The Star News Shops deal, subject to pensions regulator approval, will add 150 CTN stores to the portfolio.