The game is available in four episodes. The first two weigh in at 1.5GB each and cost around 1,200 Microsoft Points, or about £10 each. Episodes three and four will follow later.
Eidos reckons 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 is a remake of the original Tomb Raider at a basic level, but has been given a complete makeover and a lot more extras.
"We have created this version of Anniversary specifically for digital distribution as episodic content," said Jane Cavanagh, chief executive at Eidos.
"This is part of our strategy to grow our presence in online and digital distribution as we believe there are huge opportunities in this format and we intend to capitalise on the increasing demand for digitally downloaded content.
"Lara has always been at the forefront of technology and this world first with Microsoft highlights that fact. Ultimately we also intend to make the title available at retail so that it reaches the maximum possible audience."
The market for digitally downloaded core PC and console games is expected to exceed $289m by 2010, with games-on-demand services topping $104m, according to Screen Digest.
Microsoft's Xbox Live online gaming network already boasts over 2.3 billion hours of online gaming since its launch in 2004.
Xbox 360 owners have activated more than five billion points (over $60m) on Xbox Live Marketplace with over 135 million downloads since the launch of Xbox 360 in 2005.
Cotton seedling freezes to death as Chang'e-4 shuts down for the Moon's 14-day lunar night
Fortnite easily out-earns PUBG, Assassin's Creed Odyssey and Red Dead Redemption 2 in 2018
Meteor showers as a service will be visible for about 100 kilometres in all directions
Saturn's rings only formed in the past 100 million years, suggests analysis of Cassini space probe data
New findings contradict conventional belief that Saturn's rings were formed along with the planet about 4.5 billion years ago