An electro-hydraulic actuator for actuating a brake caliper may have an electric motor with a drive shaft, a transforming mechanism and a first housing to accommodate the transforming mechanism and support a second housing of the electric motor. The transforming mechanism may include a reduction gear to demultiply the rotary motion of the drive shaft. The reduction gear may have a crown with inner toothing in one piece and that is rotationally locked. The crown may have a front portion directly shape-coupled to and inserted in the second housing of the electric motor and a connection integral with the first housing of the transforming mechanism for a precise centering between the electric motor and the reduction gear with respect to the axis of the drive shaft and with respect to a central axis of the reduction gear.