Wireless edge caching alleviates the capacity burden imposed on the backhaul of dense cellular networks while reducing the user-perceived latency. In this paper, we consider the joint optimization of caching and user association (JCA) policies with respect to the total cache hit ratio, taking into account the limited radio and storage resources, the service requirements, and the quality of the wireless channels. In order to effectively capture the dynamic nature and randomness of the system under study, which is reflected respectively in the mobility and content preferences of the users as well as in the time-variance of the wireless channels due to fading, we use a stochastic optimization framework based on Lyapunov optimization. After formulating the corresponding dynamic JCA problem, we solve this NPhard task by applying a low-complexity heuristic algorithm that alternates at each timeslot between the caching and user association problems. Numerical simulations highlight the performance gains of the proposed dynamic JCA scheme over its static and decoupled caching/user association counterparts and shed light on the effect of various parameters on the performance.