In this paper we address the problem of driving a group of agents towards a consensus point when agents have a discrete-time integrator dynamics and the communication graph is time-varying. We propose two decentralized Model Predictive Control (MPC) schemes that take into account constraints on the agents’ inputs and show that they guarantee consensus under mild assumptions. Since the global cost does not decrease monotonically, it cannot be used as a Lyapunov function for proving convergence to consensus. Rather, our proofs exploit geometric properties of the optimal path followed by individual agents.