Recently, a new procedure to quantize the SU(N) Yang-Mills theory in the nonperturbative regime was proposed. The idea is to divide the configuration space {Aμ} into sectors labeled by different topological degrees of freedom and fix the gauge separately on each one of them. As Singer's theorem on gauge copies only refers to gauge fixing conditions that are global in {Aμ}, this construction might avoid the Gribov problem. In this work, we present a proof of the renormalizability in the center-vortex sectors, thus establishing the calculability of the Yang-Mills center-vortex ensemble.