Microsoft has officially announced that Call of Duty: Black Ops 1 is (finally) now available via backwards compatibility on Xbox One.
— Xbox (@Xbox) May 17, 2016
In order to play Black Ops 1, players must own a copy of the title — either a digital download or a disc version — on Xbox 360. If you own a digital download, the title should appear in your Xbox One’s Games Library. If you own a disc, you must put the disc in the tray in order to play.
With backwards compatibility, players are able to play the entire base game as well as all of the DLC packs. In order to play the DLC packs, players must own the DLCs. You can visit the Xbox Marketplace online or check on the Xbox One Store to buy the DLCs if you do not already own them.
Players must own Xbox Live Gold membership in order to play online. As you are playing on the Xbox 360 servers, all stats and data — as along as you are on the same Xbox Live account — should still be available on the Xbox One console.
Visit Xbox.com to learn more about Backwards Compatibility.