A transmission driving device that is capable of preventing displacement of a shift operation member or a select operation member in a case where there is reverse input in the shift operation member or the select operation member by inhibiting rotation of a rotation member which is released from an input shaft. When an input shaft and a first rotor are connected, the first electromagnetic coil is an excitation state and a second electromagnetic coil is in a non-excitation state. In this state, a second magnetic ring is not attracted to the side of the second electromagnetic coil, a seventh facing, which is fixed to the second magnetic ring, and an eighth facing are engaged with each other, and a second rotor and a casing are connected to each other. In a connection state of the second rotor and the casing, the second rotor cannot be rotated.