We will introduce the Rohlin property for a centrally free cocycle action of an amenable C*-tensor category on a von Neumann algebra. Our main result says two centrally free cocycle actions are cocycle conjugate if they are approximately unitarily equivalent. This generalizes the classification of them due to Izumi and Masuda for a fusion category and a strongly amenable C*-tensor category, respectively. We also discuss how we can recover Popa`s celebrated classification result of amenable subfactors.