The authors [1] have recently constructed models of nonextensive black hole Thermodynamics from a generalized Wick’s rotation procedure in the evaluation of the Euclidean path integral. We have explicitly shown in [6] how the Schwarzschild Black Hole Entropy (in all dimensions) emerges from truly point mass sources at r = 0 due to a non-vanishing scalar curvature involving the Dirac delta distribution. It is the density and anisotropic pressure components associated with the point mass delta function source at the origin r = 0 which furnish the Schwarzschild black hole entropy in all dimensions D ≥ 4 after evaluating the non-vanishing Euclidean Einstein-Hilbert action. In this work we generalize our construction of the Euclidean Einstein-Hilbert action by following the generalized Wick’s rotation procedure of [1] in order to construct the nonextensive Schwarzschild black hole entropies in all dimensions. The first law of Thermodynamics is obeyed and when the nonextensivity parameter is λ < 0, the nonextensive entropy is finite at T = 0 despite that the Bekenstein-Hawking entropy S_BH (β = ∞) = S_BH (T = 0) = ∞ blows up violating the the third law of Thermodynamics.