Controller Area Network (CAN) is the most frequently used in-vehicle communication system in the automotive industry today. The communication inside the CAN bus is typically encoded using proprietary formats in order to prevent easy access to the information exchanged on the bus. However, it is still possible to decode this information through reverse engineering, performed either manually or via automated tools. Existing automated CAN bus reverse engineering methods are still time-consuming and require some manual effort, i.e., to inject diagnostic messages in order to trigger specific responses. In this paper, we propose CANMatch a fully automated CAN bus reverse engineering framework that does not require any manual effort and significantly decreases the execution time by exploiting the reuse of CAN frames across different vehicle models. We evaluate the proposed solution on a dataset of CAN logs, or traces, related to 479 vehicles from 29 different automotive manufacturers, demonstrating its improved performance with respect to the state of the art.