No. The Xbox One controller **cannot** connect to or function on an Xbox 360.
| Controller | Xbox 360 | Xbox One | Series X|S | PC (Windows) |
|---|---|---|---|---|
| Xbox 360 Wireless | ✅ Native | ❌ | ❌ | ✅ (Wireless Receiver / Wired) |
| Xbox 360 Wired | ✅ Native | ❌ | ❌ | ✅ Native |
| Xbox One Wireless | ❌ | ✅ Native | ✅ Native | ✅ (Bluetooth / Dongle / USB) |
| Series X|S Wireless | ❌ | ✅ Native | ✅ Native | ✅ (Bluetooth / Dongle / USB) |
Stick to 360 controllers on 360. They're cheap, plentiful, and the d-pad transforming model (late revision) is excellent.