In combination with a belt tensioner which includes an idler pulley to be radially displaced under control of an actuator for applying an tensioning force on an endless belt of the drive system for the vehicle accessories, an electric control apparatus comprises a microcomputer for calculating the actual tensioning force on the belt related to radial displacement of the idler pulley and for calculating drive power necessary for driving the vehicle accessories to calculate total drive torque of the vehicle accessories in relation to rotational speed of a prime mover of the vehicle. The microcomputer also calculates an optimum tensioning force based on a desired relationship between the optimum tensioning force and the total drive torque in consideration with the maximum efficiency of power transmission of the belt such that it generates a control signal when the calculated actual tensioning force is different from the calculated optimum tensioning force. An electrically operated drive mechanism is responsive to the control signal from the microcomputer to operate the actuator in accordance with the difference between the calculated actual and optimum tensioning force.