Among the recently discovered iron-based superconductors, ultrathin films of FeSe grown on SrTiO3 substrates have uniquely evolved into a high superconducting-transition-temperature (TC) material. The mechanisms for the high-TC superconductivity are ongoing debate mainly with the superconducting gap characterized with in-situ analysis for FeSe films grown by bottom-up molecular-beam epitaxy. Here, we demonstrate the alternative access to investigate the high-TC superconductivity in ultrathin FeSe with top-down electrochemical etching technique in three-terminal transistor configuration. In addition to the high-TC FeSe on SrTiO3, the electrochemically etched ultrathin FeSe transistor on MgO also exhibits superconductivity around 40 K, implying that the application of electric-field effectively contributes to the high-TC superconductivity in ultrathin FeSe regardless of substrate material. Moreover, the observable critical thickness for the high-TC superconductivity is expanded up to 10-unit-cells under applying electric-field and the insulator-superconductor transition is electrostatically controlled. The present demonstration implies that the electric-field effect on both conduction and valence bands plays a crucial role for inducing high-TC superconductivity in FeSe.