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 Cr₂Te₃ is a ferromagnetic, quasi-two-dimensional layered material with perpendicular magnetic anisotropy, strong spin-orbit coupling, and non-trivial band topology. Applying density functional theory (DFT) and maximally localized Wannier functions (MLWFs), we extract values for the exchange coupling constants and magnetic anisotropy for a model magnetic Hamiltonian and we determine the band topological properties resulting in the anomalous Hall effect (AHE) as a function of strain. We find that Berry curvature switches sign under compressive strain, which results in a sign change in the anomalous Hall conductivity. The underlying mechanism for the strain-induced sign change is a large contribution to the Berry curvature resulting from two nearly degenerate, anti-crossing Cr-bands along high-symmetry paths in the Brillouin zone. These theoretical results are in agreement with the recent experimental results demonstrating that the intrinsic Berry phase mechanism is the primary origin of AHE in Cr₂Te₃ [1].