Having been teased a short time ago, Xbox's Mike Ybarra has confirmed that those in the preview program and on the New Xbox One Experience trial will be getting controller remapping in the latest build which should be starting to hit consoles. He confirmed the news on Twitter:
Yes, controller button remapping is in this latest build. You can find it in settings/kinect&devices/devices&accessories.— Mike Ybarra (@XboxQwik) October 14, 2015
He also confirmed it works for all controllers (which is good considering the Elite hasn't launched yet) so if you're in the program follow the instructions above and get to it!
Let us know how it works for you in the comments below.