Parsons has spent the last three years as a commercial director at Ashley Chase, producer of the Ford Farm cheese brands.
Prior to this, he spent more than seven years at Dairy Crest.
Parsons said he was excited to join Cricketer because of its expertise in full flavoured low-fat cheeses, which have won contracts with most of the major multiples. "This is testament to the fine quality of its cheese and the traditional skills of Cricketer's cheesemakers," he said.
Departing MD Paddy O'Keeffe said: "I am very pleased to be leaving Cricketer Farm in such excellent hands." O'Keeffe remains a director of Cricketer and will be MD of the company's new Yorkshire-based sister company, St Helen's Farm.