Source: Valve
While it's possible to use the new Steam Machine with a traditional Bluetooth controller, Valve introduced a new Steam Controller. The controller integrates the different control methods you get on a Steam Deck, including sticks, grip buttons, triggers, face buttons, and bumpers. There are also trackpads for mouse controls and gyro controls.
You can use the Steam Controller wired or through Bluetooth. The charging dongle acts as a wireless transmitter for faster potential connection. You can individually customize input for each game, with profiles that are shareable. The accessory isn't limited to use with the Steam Machine. It will also work with the Steam Deck and Steam Frame VR. Valve has yet to announce the price for the controller.