In this paper, we consider finite model approximations of team problems where the finite models are constructed through uniform quantization of the observations of the agents. Strategies obtained from finite models are shown to approximate the optimal cost with arbitrary precision under mild technical assumptions. An analogous result is separately proved for the Witsenhausen's celebrated counterexample. For this counterexample, our approximation approach provides the first rigorously established result, to our knowledge, that for any ε > 0, one can construct an ε-optimal strategy through an explicit solution of a simpler problem.