An electric drive device for an electric power steering system, comprising an electric motor with a motor case, a stator arranged inside the motor case providing a plurality of phases, a rotor arranged rotatably in relation to the stator, and a motor shaft that rotates together with the rotor with a drive end of the output torque of the motor projecting from the motor case; an electronic control unit arranged after the motor which controls the drive of said motor and comprises a power board supplying current to the motor, and a control board electrically connected to the power board which controls the drive of the motor through the power board; and a heat sink (40; 40') absorbing and dissipating the heat generated by the power board; the heat sink (40; 40'), the power board and the control board being arranged after the motor in the mentioned order, the power board covering the cross section of the motor case and the device comprising a connector which allows connecting the electronic control unit with the outside by wiring, characterized in that said connector comprises a power supply housing for receiving power from the outside, an electric torque signal housing for receiving the electric torque signal from the outside, and a communications housing for reciprocal communications with the outside, and terminals (84, 85, 86) which allow directly connecting said connector with the power board and with the control board, wherein the connector is attached to the device laterally from the outside, said connector comprising a first area which is attached to the device, said first area comprising the terminals (84, 85, 86), and a second area, attached to the first area, comprising the power supply housing, the electric torque signal housing and the communications housing, the first area comprising a plurality of protrusions projecting in a plane perpendicular to the geometric axis of the motor shaft, and the heat sink (40; 40') comprising a plurality of housings in a peripheral edge, said housings of the heat sink (40; 40') allowing the housing of the protrusions of the first area and preventing the extraction of the protrusions in the radial direction, wherein the heat sink (40; 40') comprises in its outer side (47; 49) a vertical edge running along the periphery in a segment which is not attached to the connector, and the connector comprises a vertical edge in the first area running along the area of intersection with the second area, the ends of the vertical edge of the heat sink (40; 40') and the ends of the vertical edge of the connector coinciding when the connector is assembled in the heat sink (40; 40'), the heat sink (40; 40') comprising a plurality of seats with holes in the periphery of the outer side (47; 49), and the motor case comprising at one end of its side wall a plurality of seats with holes coinciding with the holes of the outer side (47; 49) of the heat sink (40; 40'), the device comprising a cover which comprises seats with holes projecting radially from their end and allowing the cover to cover the electronic control unit when said cover is assembled against the motor case, attaching the seats of the cover to the seats of the heat sink (40; 40') with attachment means, the cover overlapping the vertical edge of the heat sink (40; 40') and the vertical edge of the connector.