For multivariable discrete-time systems described by transfer matrices, we develop a hierarchical least squares iterative (HLSI) algorithm and a hierarchical least squares (HLS) algorithm based on a hierarchical identification principle. We show that the parameter estimation error given by the HLSI algorithm converges to zero for the deterministic cases, and that the parameter estimates by the HLS algorithm consistently converge to the true parameters for the stochastic cases. The algorithms proposed have significant computational advantage over existing identification algorithms. Finally, we test the proposed algorithms on an example and show their effectiveness.