TellTale Games confirmed the news on Twitter, revealing that the first part of the episodic adventure will be free until January 31.
Users can purchase the subsequent four episodes for 400 Microsoft Points (£3.40 / $5) each.
TellTale Games is also giving away the first episode of its survival horror adventure game to iPhone and iPad users.
Episode 1: A New Day introduces main character Lee Everett, who encounters the zombie outbreak while on his way to prison on murder charges. Soon he finds himself protecting the 8-year-old girl Clementine, both from zombies and from other survivors.
The Walking Dead was recently voted Digital Spy's 2012 game of the year, beating the likes of Far Cry 3, Black Ops 2 and XCOM: Enemy Unknown.
Download The Walking Dead - Episode 1: A New Day for free on Xbox 360 here.
> Why 'The Walking Dead' is Digital Spy's 2012 Game of the Year
> Game of the Year 2012: Digital Spy picks the most memorable moments
Watch the trailer for The Walking Dead - Episode 1: A New Day below: