Collect all the tools you will need for this project. You will also need the 2.5mm controller patch cable from your old headset, and the new headset from your Xbox One.
Disassemble your new Xbox One headset, or simply cut the cable near the mic/speaker.
Cut one end off of the the small headphone cord from your Xbox 360 Headset.
Strip the wires so you can clearly separate and identify each one for both cables. There will be 3 wires from the 360 cable (Red, White and Gold [or Green, Red and Gold]) and 4 wires from the Xbox One Cable (Blue, White, Black and Gold).
Splice the wires in the following Xbox360 - XboxOne pairs: White - White Red - Blue Gold - Black & Gold
Or (with newer Xbox360 Cables)
Red-White Green-Blue Gold-Black & Gold
Keep the wires separated and gently wrap them with electrical/duct tape. Then enjoy your new adapter cable!