Label shift, which investigates the adaptation of label distributions between the fixed source and target domains, has attracted significant research interests and broad applications in offline settings. In real-world scenarios, however, data often arrives as a continuous stream. Addressing label shift in online learning settings is paramount. Existing strategies, which tailor traditional offline label shift techniques to online settings, have degraded performance due to the inconsistent estimation of label distributions and violation of convex assumption for theoretical guarantee. In this paper, we propose a novel method to ensure consistent adaptation to online label shift. We construct a new convex risk estimator that is pivotal for both online optimization and theoretical analysis. Furthermore, we enhance an optimistic online algorithm as the base learner and refine the classifier using an ensemble method. Theoretically, we derive a universal dynamic regret which achieves minimax optimal. Extensive experiments on both real-world datasets and human motion task demonstrate the superiority of our method comparing existing methods.