An electric driving device for a transmission can be reduced in size with a simple structure, and can be installed in a small-sized car, such as a passenger car. In this electric driving device, a shift shaft 2 effects a selecting operation by its displacement in the axial direction and a shifting operation by its rotation. The displacement of the shift shaft 2 in the axial direction is effected by rocking and displacing a rocking arm 18 by means of a first actuator 13 or 113. Rotation of the shift shaft 2 is effected by pushing and/or pulling a rocking arm 20 by means of a second actuator 21. This driving arm 20 is fixedly disposed on the outer peripheral surface of a spline tube 5 which is brought into spline-engagement with the shift shaft 2.