Matthews will join the company on 1 December and work alongside Mooney until he steps down on 30 April, ending six years at Punch Graphix and a printing career that began in 1972.
Mooney said: "I am already beginning to look back on a very enjoyable career in the industry.
"I have had the pleasure of both working with and meeting some very pleasant people throughout my 36 years in print. It has been a particular pleasure to work with some great individuals.
"Chris will certainly bring additional strength to our sales efforts in the UK and that will be his first area of focus during December."
Matthews will officially take the helm at Punch on 1 January.
Punch Graphix's Mooney to retire from industry
Punch Graphix UK managing director David Mooney has said he will retire next year and will be replaced by Heidelberg and Kodak veteran Chris Matthews.