A new feature for Xbox One has now been launched according to Major Nelson. Now you can customise and remap the buttons for the regular Xbox One controllers to get the settings you prefer. This works with both first- and third party controllers.
The controller remapping can be accessed in three ways with the new Xbox One dashboard that was released last week:
1. Settings / Kinect & Devices / Devices & Accessories
2. Settings / Ease of access / Button mapping
3. Launch the Xbox Accessories app directly
If you want more specific instructions on how to remap, head over to Major Nelson who has all the details.