The combined group will continue to operate both the Game and Gamestation formats - a total of 627 stores across the UK and Ireland.
Game said the acquisition was in line with its strategy to expand its customer reach, both within the UK and internationally.
The deal is expected to be earnings enhancing in the first full year and deliver£7 million of synergies a year by the second full year.
The existing Gamestation senior management team will remain within the enlarged group.
Game chairman Peter Lewis said: 'The Gamestation business is one we have long admired and is complementary to our existing business in terms of both store portfolio and target customer.'
In a statement, Game said the deal was secured with Blockbuster on an unconditional basis and acknowledged that the regulatory authorities would have the opportunity to review the acquisition.
Gamestation reported revenues of£203.5 million and a profit before tax of£2.1 million in the year to December 31.
Gamestation's parent company US-based Blockbuster Inc first revealed its intention to offload the chain in 2005. It saw the business as a non-core asset and wanted to focus on improving its domestic operation, where sales have been sliding.
As a result of the acquisition, Game will incur one-off costs of£4 million, plus an additional£4 million of incremental capital expenditure on IT and logistics.