The campaign, run by Flytxt on behalf of Universal Pictures International, is the first that the entertainment giant has run on a multi-country basis.
It will invite people to take part in a five-day "Do you have what it takes to be Bourne?" challenge, which will see tasks and clues being sent to mobiles on a daily basis.
People will be encouraged to participate, with the chance to win film-related prizes and automatic entry into regional prize draws. It launches in Australia this month, and is due to hit the UK in January, with Italy, Germany, France, Mexico and Sweden also slated to participate.
Julia Howe, vice-president of feature film at Universal Pictures International, said: "We're excited about the mobile campaign and how it will bring the film to life and build a connection between the consumer and the Jason Bourne character. We look forward to measuring the effectiveness of such a direct and personal channel."
'The Bourne Supremacy' centres around the character Jason Bourne, played by Damon, who is framed for a botched CIA operation and is forced to take up his former life as an assassin to survive.
The DVD launch will be backed with online and offline advertising, including television and outdoor ads.
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