Included in the list of eligible games are FIFA 14, Assassins Creed IV: Black Flag, Call of Duty: Ghosts, Battlefield 4 and Watch Dogs.
Exactly how you score your cheap upgrade is where things get complicated. According to Best Buy's official site, if you purchase one of the above games within a set period after its release (most can be picked up as much as a month after release day), you'll be given a $10 coupon to be put toward your game's Xbox One incarnation. When you want to upgrade, you must present this coupon as well as the Xbox 360 game. Best Buy will then give you $40 store credit in exchange for the game, reducing the final cost of your new Xbox One game to $10 (unless the Xbox One version has a retail price greater than $60; in that case you'll be paying the remainder as well).
If this scheme sounds intriguing, you should also note that all such upgrades must occur by December 31. Full legal details and all the fine print you can digest can be found on Best Buy's official site.