To provide a controller for AC rotary electric machine and an electric power steering apparatus which can superimposes a cancellation current for canceling the torque ripple component on the winding current in feedforward manner and cancel the torque ripple component. A controller for AC rotary electric machine calculates an oscillation voltage command value of q-axis which has the same frequency as the torque ripple component; calculates a reverse phase of the torque ripple component based on the current information and the magnetic pole position; calculates a correction phase corresponding to the phase delay of the actual current with respect to the oscillation voltage command value of q-axis; and sets a phase of the oscillation voltage command value of q-axis to a phase obtained by advancing the reverse phase of the torque ripple component by the correction phase.