The present era is marked by rapid improvement and advances in technology. One of the most essential areas that demand improvement is the traffic signal, as it constitutes the core of the traffic system. This demand becomes stringent with the development of Smart Cities. Unfortunately, road traffic is currently controlled by very old traffic signals (tri-color signals) regardless of the relentless effort devoted to developing and improving the traffic flow. These traditional traffic signals have many problems including inefficient time management in road intersections; they are not immune to some environmental conditions, like rain; and they have no means of giving priority to emergency vehicles. New technologies like Vehicular Ad-hoc Networks (VANET) and Internet of Vehicles (IoV) enable vehicles to communicate with those nearby and with a dedicated infrastructure wirelessly. In this paper, we propose a new traffic management system based on the existing VANET and IoV that is suitable for future traffic systems and Smart Cities. In this paper, we present the architecture of our proposed Intelligent Traffic Management System (ITMS) and Smart Traffic Signal (STS) controller. We present local traffic management of an intersection based on the demands of future Smart Cities for fairness, reducing commute time, providing reasonable traffic flow, reducing traffic congestion, and giving priority to emergency vehicles. Simulation results showed that the proposed system outperforms the traditional management system and could be a candidate for the traffic management system in future Smart Cities. Our proposed adaptive algorithm not only significantly reduces the average waiting time (delay) but also increases the number of serviced vehicles. Besides, we present the implemented hardware prototype for STS.