An electric brake booster includes an electric motor activating a booster piston acting on the master-cylinder during brake pedal activation. The booster piston is driven in the direction of the action of same on the master-cylinder by an electric motor linked to a mechanical transmission that includes a screw held by the motor shaft. The screw meshes with two symmetrical worm gears that are integral with respective transmission shafts housed in a bearing of the body of the brake booster. The two shafts each carry a spur gear that meshes with a rack of the booster piston. The shafts are free in translation relative to the screw and to the body of the electric brake booster but are integral with each other in the translational movement of same. The shafts are integrally connected in translation by a coupling member formed by a crosspiece carrying two rotation bearings.