Most telerobotic applications rely on a Human-Robot Interface that requires the operator to continuously monitor the state of the robot through visual feedback while uses manual input devices to send commands to control the navigation of the robot. Although this setup is present in many examples of telerobotic applications, it may not be suitable in situations when it is not possible or desirable to have manual input devices, or when the operator has a motor disability that does not allow the use of that type of input devices. Since the operator already uses his/her eyes in the monitoring task, an interface based on the inputs from their gaze could be used to teleoperate the robot. This paper presents a telerobotic platform that uses a user interface based on eye-gaze tracking that enables a user to control the navigation of a teleoperated mobile robot using only his/her eyes as inputs to the system. Details of the operation of the eye-gaze tracking system and the results of a task-oriented evaluation of the developed system are also included.