Routing strategies using dynamic traffic assignment have been proposed in the literature to optimize system performance. However, challenges have persisted in their deployability and effectiveness due to inherent strong assumptions on traveler behavior and availability of network-level real-time traffic information, and the high computational burden associated with computing network-wide flows in real-time. To address these gaps, this study proposes an incentive-based decentralized routing strategy to nudge the network performance closer to the system optimum in a traffic system with connected and autonomous vehicles (CAVs). The strategy consists of three stages. The first stage incorporates a local route switching dynamical system to approximate the system optimal route flow in a local area based on vehicles’ knowledge of local traffic information. This system is decentralized in the sense that it only updates the local route choices of vehicles in this area to circumvent the high computational burden associated with computing the flows on the entire network. The second stage optimizes the route for each CAV by considering individual heterogeneity in traveler preferences (e.g., the value of time) to maximize the utilities of all travelers in the local area. Constraints are also incorporated to ensure that these routes can achieve the approximated local system optimal flow of the first stage. The third stage leverages an expected envy-free incentive mechanism to ensure that travelers in the local area can accept the optimal routes determined in the second stage. They prove that the incentive mechanism is expected individual-rational and budget-balanced. The study analytically shows that the proposed incentive-based decentralized routing strategy can enhance network performance and user satisfaction in a connected and autonomous traffic environment.