This paper presents the adaptive design of an antomatic voltage regulator (AVR) control scheme for synchronous generators that is capable of providing satisfactory voltage control performance in the presence of unknown variations of the power system operating conditions. The design is articulated in four steps: voltage and current phasor estimation, estimation of the parameters of the Thevenin equivalent circuit adopted to represent the power system response using a steady-state model, determination of the sampled-data transfer function of the system, and AVR design developed according to discrete-time techniques. A suitable procedure is described to derive the sampled-data transfer function of the system starting from models of the power system, synchronous generator, and exciter. The obtained transfer function depends on the estimated parameters yielded by a recursive least-squares algorithm subject to constraints deriving from the Thevenin circuit. The AVR design is based on the pole-assignment technique while the phasors estimation is performed by two Kalman filters. Finally, the results of accurate numerical simulations conducted for a test network are reported, comparing the performance of the proposed adaptive control scheme to the one of a PID controller with fixed parameters.