Weighing in at 3.81 GB, the title is normally priced at £14.99 / $19.99 on Microsoft's digital marketplace.
CVG's Dark Souls review concluded: "Its stupefying breadth will surely capture your imagination like few other worlds you've explored in games - and because of that, Dark Souls is, simply, an RPG to die for."
June's Xbox 360 Games with Gold offering will also include free Charlie Murder and Super Street Fighter IV downloads, from the 16th-30th of the month.
Games with Gold will launch on Xbox One later this month with Max: The Curse of Brotherhood and Halo: Spartan Assault.
A single Gold membership will provide owners with access to the free games for both Xbox 360 and Xbox One, although the service will differ on the two consoles in one important way. On Xbox 360, users are still granted access to free game downloads even if their subscription lapses, but on Xbox One, users will be required to maintain their subscription in order to access freely downloaded games.
Microsoft will no longer gate entertainment apps behind a Gold subscription following a June system update. It will offer a refund to current subscribers who no longer wish to use the service in light of the upcoming changes.