Whiteside, who headed the Thresher Group from 2004-2007, was replaced by Yvonne Rankin after the chain was bought by private equity firm Vision Capital.
He is to take over from Deborah Kemp, who has been with Punch for 25 years, on Nov 3.
After Whiteside left Thresher Group he became a non-executive director of baker Greggs. His background includes working for Marks & Spencer and Ocado.
Punch chief executive Giles Thorley said: "Roger has a long and diverse career in the retail sector and brings with him exceptional experience which will be invaluable to the group in taking our leased business to the next stage of its development."