The Xbox One version of Fallout 4 supports mods starting today, something never seen before on consoles. There are currently 877 mods available, with more possibly coming in a near future.
Mods will be limited to a 2GB download, however, Bethesda admits they may increase the download limit at some point. When you load a mod and save your game, this save file will be added to a special section, which means that the player will have the original save and a modded save. Players will need to reboot the game when enabling or disabling mods.
Similar to how it works on PC, the load order might be crucial in order for the game run properly as some mods may require other mods to work. Obviously, using mods will prevent players from earning Achievements.
You can check the full list of mods here.