A hydrostatic actuator and an arrangement for attaching it to a receiving component are provided. The hydrostatic actuator has a master cylinder containing a housing and a piston movable axially within the housing which acts on a pressure chamber filled with a pressurizing agent. The piston is driven by a rotary-driven electric motor having a stator and a rotor, by a rolling planetary transmission that converts the rotary drive to an axial motion. In order to be able to produce such a hydrostatic actuator with little need for construction space, cost-effectively and with better quality, a supporting of the rolling planetary transmission is simplified, and the cooling and shielding of an electronic controller and the pressure behavior of the hydrostatic actuator is improved.