A suitable control architecture for connected vehicle platoons may be seen as a promising solution for today’s traffic problems, by improving road safety and traffic flow, reducing emissions and fuel consumption, and increasing driver comfort. This paper provides a comprehensive overview concerning the defining levels of a general control architecture for connected vehicle platoons, intending to illustrate the options available in terms of sensor technologies, in-vehicle networks, vehicular communication, and control solutions. Moreover, starting from the proposed control architecture, a solution that implements a Cooperative Adaptive Cruise Control (CACC) functionality for a vehicle platoon is designed. Also, two control algorithms based on the distributed model-based predictive control (DMPC) strategy and the feedback gain matrix method for the control level of the CACC functionality are proposed. The designed architecture was tested in a simulation scenario, and the obtained results show the control performances achieved using the proposed solutions suitable for the longitudinal dynamics of vehicle platoons.