This is the first time that the serialisation of a full retail game will be available for purchase through Xbox Live Marketplace.
Tomb Raider: Anniversary will be available in four parts, episodes one and two in September and episodes three and four shortly afterwards.
Jane Cavanagh, chief executive at Eidos, said that the move was part of the company's strategy to "grow our presence in online and digital distribution".
Xbox 360 players will require a Tomb Raider Legend disc to access the Tomb Raider: Anniversary downloadable content.
The episodes will cost 2,400 Microsoft Points for all four episodes, and will be released in two separate launches. A full retail version is planned for Xbox 360 later this year.
Xbox 360 owners have clocked up over 135 million downloads since the launch of the console in 2005.
The market for digital download of core PC and console games is expected to exceed $289m by 2010, according to ScreenDigest, with games on demand services topping $104m.
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