Wild, 67, who helmed Domino's Pizza Group Plc for five years before retiring in 2019 was also the top boss of bike and motor parts retailer Halfords for about four years until 2012.
"I am delighted to have the opportunity to play a role in driving the future success of the business, blending my prior experiences in Domino's and Poland to drive value for all stakeholders," Wild said in a statement.
Wild succeeds Nick Donaldson, 69, who retired on 31 December after 12 years as chairman of the company.
DP Poland, the Polish master franchisee for US-based Domino's Pizza Inc, holds rights to develop and sub-franchise its pizza stores in Poland and Croatia. It currently has more than 120 stores across the region.
The company's non-executive director, Przemyslaw Glebocki, has been appointed as interim chair until Wild takes over in early 2023.