An engine starting apparatus is equipped with a starter which, when it is required to start an engine, moves a pinion to establish engagement with a ring gear coupled to the engine and energizes an electric motor to produce and transmit torque to the ring gear through the pinion for cranking the engine. When the rate of decrease in current flowing in the electric motor or the rate of rise in voltage appearing at a terminal of the starter or a power supply for the electric motor exceeds a given value after the engine starts being cranked, the engine starting apparatus works as a firing-up determiner to determine that the engine has been fully fired up.