A concurrent learning adaptive control architecture for uncertain linear switched dynamical systems is presented. Like other concurrent learning adaptive control architectures, the adaptive weight update law uses both recorded and current data concurrently for adaptation. In addition, a verifiable condition on the linear independence of the recorded data is shown to be sufficient to guarantee global exponential stability and adaptive weight convergence. Furthermore, it is shown that the recorded data eventually meets this condition after a system switch without any additional excitation from the exogenous reference input or knowledge of the switching signal if there is sufficient time in between switches. That is, after a switch, the system will be automatically excited and sufficiently rich data will be recorded. As a result, data that is irrelevant to the current subsystem will be overwritten. Thus, reference model tracking error and adaptive weight error will eventually become globally exponential stable for all switched subsystems. Numerical examples are presented to illustrate the effectiveness of the proposed architecture.