Vehicle platooning has great potential for the reduction of greenhouse gas emissions and fuel consumption of heavy-duty vehicles. However, previous works on fuel-efficient platoon control largely ignore the effect of gear changes, even though experimental studies have shown that gear shifts have a large impact on the behavior and fuel consumption of vehicle platoons. In particular, the interruption in traction force during a gear shift can cause large deviations in the tracking of the reference speed and inter-vehicle distance and can result in the braking of the vehicles. In this paper, we discuss a control architecture that includes the management of gear shifts and we propose a method to select the gears that takes fuel-efficiency into account, but also targets the good behavior of the platoon. In detail, the proposed method is based on a dynamic programming formulation that computes the optimal sequence of gear shifts necessary for the fuel-efficient and smooth tracking of a given reference speed profile. The performance of the proposed approach is finally analyzed by means of simulations by comparing it with the performance of alternative solutions.