The store stocks non-Hamleys brands but has never had another retailer operating within the shop before.
A Game spokeswoman said: 'Game sees this as a great opportunity, as previously Hamleys has not been able to maximise the opportunity that exists with games.'
The 1,500 sq ft (140 sq m) concession is in the basement of the store, in place of the Sega Arcade.
Game is Europe's leading retailer of computer software and video games and operates from more than 600 stores, concessions and franchises in the UK, Eire, Sweden, Denmark, Spain and France.
In 1994, Hamleys of London was listed on the London Stock Exchange and became Hamleys plc. It remained a public company for 9 years until 2003 when, with the support of Baugur, the Iceland-based retail group, Hamleys' management team took the company private.