Dennett said it had been a "privilege" to serve the co-operative, but was looking ahead to a new chapter in his career.
Travel and post office operations manager Dennett will be succeeded by interim head of retail Shaun Davies.
Davies, who himself has more than 30 years' retail experience, will take operational responsibility for travel and post office.
Dennett will leave his post at the end of January.
“It has been a privilege to spend three decades with this business, growing alongside the teams and customers who make it such a special place to work," he said.
