We study the mobility-aware computation offloading design for mobile edge computing (MEC) based vehicular wireless networks which considers random mobility of the vehicle and its potential handover during the offloading process. The computation offloading decision is made by comparing the average total costs due to the local and remote computation task executions at the vehicle and the MEC servers, respectively. Toward this end, we propose an analytical model to determine the average total cost due to remote task execution. We evaluate the performance of the proposed design by comparing its achievable cost with that due to an average mobility-based approximation. Simulation results show a cost reduction of up to 17% compared to the baseline.