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An analytical study of the behavior of the voter model on the small-world topology is performed. In order to solve the equations for the dynamics, we consider an annealed version of the Watts-Strogatz (WS) network, where long-range connections are randomly chosen at each time step. The resulting dynamics is as rich as on the original WS network. A temporal scale τ separates a quasistationary disordered state with coexisting domains from a fully ordered frozen configuration. τ is proportional to the number of nodes in the network, so that the system remains asymptotically disordered in the thermodynamic limit.