DLC for backwardly compatible Xbox 360 games will work on Xbox One, but a tiny hoop must be jumped through.
Xbox One's new backwards compatibility, which will be added to consoles that have upgraded to the New Experience UI tonight, is feature rich and technically impressive. However, the one thing it does not do is emulate the Xbox 360 digital store.
However, 360 DLC purchased either via an Xbox 30 console or the Xbox website will work on Microsoft's newer machine.
In addition, despite previously claiming that DLC will only be compatible on a per-publisher and per-title basis, it now seems that all backward compatible games will also support all of their DLC.
Right now, Backward Compatibility does not emulate the Xbox 360 store and new Xbox 360 games can be purchased on your Xbox 360 or via Xbox.com,” the company told Game Informer. We will support both digital and disc-based entitlements for Xbox 360 games running on Xbox One.”
Owners, obviously, must own the DLC they wish to play on Xbox One. Said content can then be installed via the Xbox One's ‘Manage Game' menu for each title.