The usage of federated learning (FL) in Vehicular Ad hoc Networks (VANET) has garnered significant interest in research due to the advantages of reducing transmission overhead and protecting user privacy by communicating local dataset gradients instead of raw data. However, implementing FL in VANETs faces challenges, including limited communication resources, high vehicle mobility, and the statistical diversity of data distributions. In order to tackle these issues, this paper introduces a novel framework for hierarchical federated learning (HFL) over multi-hop clustering-based VANET. The proposed method utilizes a weighted combination of the average relative speed and cosine similarity of FL model parameters as a clustering metric to consider both data diversity and high vehicle mobility. This metric ensures convergence with minimum changes in cluster heads while tackling the complexities associated with non-independent and identically distributed (non-IID) data scenarios. Additionally, the framework includes a novel mechanism to manage seamless transitions of cluster heads (CHs), followed by transferring the most recent FL model parameter to the designated CH. Furthermore, the proposed approach considers the option of merging CHs, aiming to reduce their count and, consequently, mitigate associated overhead. Through extensive simulations, the proposed hierarchical federated learning over clustered VANET has been demonstrated to improve accuracy and convergence time significantly while maintaining an acceptable level of packet overhead compared to previously proposed clustering algorithms and non-clustered VANET.