It is shown how a Noncommutative spacetime leads to an area, mass and entropy quantization condition which allows to derive the Schwarzschild black hole entropy A/4G, the logarithmic corrections, and further corrections, from the discrete mass transitions taken place among different mass states in D = 4. The higher dimensional generalization of the results in D = 4 follow. The discretization of the entropy-mass relation S = S ( M ) leads to an entropy quantization of the form S = S ( M_n) = n, and such that one may always assign n ``bits" to the discrete entropy, and in doing so, make contact with quantum information. The physical applications of mass quantization, like the counting of states contributing to the black hole entropy, black hole evaporation, and the direct connection to the black holes-string correspondence via the asymptotic behavior of the number of partitions of integers, follows. To conclude, it is shown how the recent large N Matrix model (fuzzy sphere) leads to very similar results for the black hole entropy as the physical model described in this work and which is based on the discrete mass transitions originating from the noncommutativity of the spacetime coordinates.