Game, which re-listed on the London Stock Exchange last June two years after falling into administration, said Smith would step down in July to join another private equity-backed retailer.
The board has brought in headhunters from Korn Ferry to find his successor.
News of Smith’s departure came as it posted a 1.8 per cent decline in pre-tax profits to £33.2m for 26 weeks to 24 January, while revenue fell 0.7 per cent to £582.1m.
Game lost as much as 50 per cent of its market value in January after issuing a shock profit warning, blaming fierce competition and increased promotional activity around Black Friday.
Despite the weak results, shareholders were nevertheless treated to a special dividend of £25m, which it said was supported by strong cash generation.