In this paper, a new predictive approach is proposed for the impedance control of bilateral drive-by-wire teleoperation systems. The proposed control structure includes two mirror predictors/observers in both: the master and slave sides. These predictors/observers are used to simultaneously estimate the master and the slave internal dynamics, and thereby to avoid the use of the delayed transmitted information. As a consequence, the influence of the delay on the whole system can be minimized and the performance can be improved. Under a set of suited hypothesis, the proposed control structure is shown to be uniformly ultimate stable even in the presence of time-varying delays. Simulation results are presented to show the effectiveness of the proposed approach. The behavior of the control structure is also experimentally demonstrated while performing remote steering of a small autonomous vehicle.