Electrostatic carrier doping using a field-effect-transistor structure is an intriguing approach to explore electronic phases by critical control of carrier concentration. We demonstrate the reversible control of the insulator-metal transition (IMT) in a two dimensional (2D) electron gas at the interface of insulating SrTiO$_3$ single crystals. Superconductivity was observed in a limited number of devices doped far beyond the IMT, which may imply the presence of 2D metal-superconductor transition. This realization of a two-dimensional metallic state on the most widely-used perovskite oxide is the best manifestation of the potential of oxide electronics.