The proliferation of compute-intensive services in next-generation vehicular networks will impose an unprecedented computation demand to meet stringent latency and resource requirements. Vehicular edge or fog computing has been a widely adopted solution to enhance the computational capacity of vehicular networks; however, the computation requirements of these compute hungry applications will surpass the capabilities of such a solution. To address this challenge, the on-board resources of neighboring mobile vehicles can be utilized. However, such resource utilization requires an incentive mechanism to motivate privately owned neighboring vehicles to participate in sharing their resources. In this paper, we propose a contract theory-based incentive mechanism that maximizes the social welfare of the vehicular networks by motivating neighboring vehicles to participate in sharing their resources. The proposed approach enables the Road Side Units (RSUs) to provide appropriate rewards by offering a tailored contract to each resource sharing vehicle based on their contribution and unique characteristics. Moreover, we derive an optimal contract scheme for computational task offloading, taking into account the individual rationality and incentive-compatible constraints. Finally, we perform numerical evaluations to demonstrate the effectiveness of our proposed scheme. The proposed scheme achieves up to 28% higher computing resource utilization, 17.2% lower energy consumption per computing resource utilization, and 17.1% lesser energy consumption per task completed when compared to the linear pricing incentive baseline.