A rotary machine driving system includes: a rotary machine including a plurality of coils; an inverter device configured to operate the rotary machine at a variable speed, including a control device for controlling power conversion by an inverter circuit, and a coil switching device for switching a connection of the coils according to the control device. The control device commands the coil switching device to switch the connection of the coils when rotation of the rotary machine transitions between a low-speed rotation range and a high-speed rotation range due to acceleration and deceleration. A starting end and a terminal end of at least one set of coils per phase of the rotary machine are drawn out in a freely connectable state. The coil switching device includes at least one movable portion driven by one actuator.