A pedal assist bicycle comprising an electric motor device that is attached to a frame of the bicycle, the frame having at least an oblique main tube, a hanger located in the anchoring zone of the rear hub to the frame, a top tube and a handlebar, said electric motor device comprising: - an electric motor that is connected to the rim of the rear wheel of the bicycle and that includes at least one free wheel for rigid connection to ear chain wheel or cassette of the bicycle, - a pedaling sensor that is connected to the hanger of the frame, - a charging outlet, and - a control unit that is connected to the frame and operated by a user for actuation and control, - wherein the electric motor device includes a block that is inserted into the oblique main tube of the frame of the bicycle, in which the block includes: - a battery, which can be recharged from the charging outlet, for actuating the motor, - a motor controller, which is connected in parallel to the battery, for controlling the operating parameters of the motor, wherein the motor controller is positioned inside the frame, - a battery manager, which is connected in parallel to the battery and to the motor controller, for managing the battery, - first cables for connecting the motor, the charging outlet and the pedaling sensor, and - second cables for connecting the control unit, - wherein the motor controller is rigidly connected to and in contact with the frame, characterized in that - the motor controller has the entire surface of the frame to discharge and dissipate the heat generated, - the said electric motor is shaped essentially similarly to the rear wheel hub, - the battery is positioned and rigidly connected inside the oblique main tube, in which said oblique main tube is only open at one end, through which the battery is inserted during the initial installation or manufacturing process, so that the battery is integrally assembled with the said oblique main tube. - an electric motor that is connected to the rim of the rear wheel of the bicycle and that includes at least one free wheel for rigid connection to ear chain wheel or cassette of the bicycle, - a pedaling sensor that is connected to the hanger of the frame, - a charging outlet, and - a control unit that is connected to the frame and operated by a user for actuation and control, - wherein the electric motor device includes a block that is inserted into the oblique main tube of the frame of the bicycle, in which the block includes: - a battery, which can be recharged from the charging outlet, for actuating the motor, - a motor controller, which is connected in parallel to the battery, for controlling the operating parameters of the motor, wherein the motor controller is positioned inside the frame, - a battery manager, which is connected in parallel to the battery and to the motor controller, for managing the battery, - first cables for connecting the motor, the charging outlet and the pedaling sensor, and - second cables for connecting the control unit, - wherein the motor controller is rigidly connected to and in contact with the frame, characterized in that - the motor controller has the entire surface of the frame to discharge and dissipate the heat generated, - the said electric motor is shaped essentially similarly to the rear wheel hub, - the battery is positioned and rigidly connected inside the oblique main tube, in which said oblique main tube is only open at one end, through which the battery is inserted during the initial installation or manufacturing process, so that the battery is integrally assembled with the said oblique main tube. - a battery, which can be recharged from the charging outlet, for actuating the motor, - a motor controller, which is connected in parallel to the battery, for controlling the operating parameters of the motor, wherein the motor controller is positioned inside the frame, - a battery manager, which is connected in parallel to the battery and to the motor controller, for managing the battery, - first cables for connecting the motor, the charging outlet and the pedaling sensor, and - second cables for connecting the control unit, - wherein the motor controller is rigidly connected to and in contact with the frame, characterized in that - the motor controller has the entire surface of the frame to discharge and dissipate the heat generated, - the said electric motor is shaped essentially similarly to the rear wheel hub, - the battery is positioned and rigidly connected inside the oblique main tube, in which said oblique main tube is only open at one end, through which the battery is inserted during the initial installation or manufacturing process, so that the battery is integrally assembled with the said oblique main tube.