Weighing in at 6.86 GB, the title is normally priced at £14.99 / $19.99 on Microsoft's digital marketplace.
CVG's Saints Row The Third review said the game, which was released in May 2012, is "wildly imaginative and frequently entertaining", but that "a lack of technical polish and weak combat overshadow its achievements".
Microsoft announced on Tuesday that June's Xbox 360 Games with Gold offering will include free Dark Souls, Charlie Murder and Super Street Fighter IV downloads.
It also said that Games with Gold will launch on Xbox One next 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 also said on Tuesday that it will no longer gate entertainment apps behind a Gold subscription beginning in June. It will offer a refund to current subscribers who no longer wish to use the service in light of the upcoming changes.