Chambers will join Game at the end of July and be responsible for the digital development of the business, which will include digital marketing.
The troubled retailer is still seeking a marketing director to replace Anna-Marie Mason, and a Game spokeswoman revealed that an announcement is expected in the "near future".
During his time at gaming media company IGN Entertainment, Chambers led the expansion of IGN into locally-operated editions of the IGN website in eleven new territories, including Arabic, Chinese and Russian speaking markets.
Chambers will report into chief executive Martyn Gibbs, who said: "We have made excellent progress over the past 12 months with our strategy to build the UK’s most valuable community of gamers and Ian will lead the next stage of our development as digital becomes the headline under which the rest of our business aligns."
Game has made a raft of changes since it was saved from administration by private investment firm OpCapita, with appointments including the hiring of former British Airways and Avios executive Fred Prego as insight director, while Benedict Smith joined as chief financial officer from Harrods.
Chambers is joining Game shortly after IGN Entertainment formed a partnership with Game that involves both firms collaborating together on digital and in-store events.
IGN-owner Ziff Davis is in the process of seeking a replacement with "broader media experience" than Chambers as it prepares to launch some of its US-based media brands such as PCMag.com in international markets.