Magnetic transition metal chalcogenides form an emerging platform for exploring spin-orbit driven Berry phase phenomena owing to the nontrivial interplay between topology and magnetism. Here we show that the anomalous Hall effect in Cr2Te3 thin films manifests a unique temperature-dependent sign reversal, resulting from the momentum-space Berry curvature as established by first-principles simulations. The sign change is strain tunable, enabled by the sharp and well-defined substrate/film interface in the quasi-two-dimensional Cr2Te3 epitaxial films, revealed by scanning transmission electron microscopy and depth-sensitive polarized neutron reflectometry. Berry phase effects also introduce hump-like Hall peaks near the coercive field, in the presence of ubiquitous magnetic domains with likely chiral spin configurations occurring during the magnetization switching process. The versatile interface tunability of Berry curvature in Cr2Te3 thin films offers new opportunities for topological electronics.