In the conventional picture of quantum feedback, control sensors make measurements on a quantum system, a classical controller processes the results of the measurements, and semiclassical actuators act back on the system to alter its behavior. We describe and provide an experimental demonstration of an alternative method for quantum feedback control, in which the sensors, controller, and actuators of conventional feedback control are replaced with quantum systems that interact coherently with the system to be controlled. The resulting control system represents a fully coherent quantum feedback loop.