Despite theoretical expectations for 2D Weyl semimetals (WSMs), realizing stable 2D topological semimetal states experimentally is currently a great challenge. Here, 2D WSM states achieved by a thickness-dependent topological phase transition from 3D Dirac semimetal to 2D WSM in molecular-beam-epitaxy-grown Bi0.96Sb0.04 thin films are reported. 2D weak anti-localization (WAL) and chiral anomaly arise in the Bi0.96Sb0.04 films for thicknesses below ≈10 nm, supporting 2D Weyl semimetallic transport in the films. This is particularly evident from magnetoresistance (MR) measurements which show cusp structures at around B = 0, indicating WAL, and negative MR, typical of chiral anomaly, only for layers with thicknesses below ≈10 nm. The temperature dependencies of the dephasing length for various thicknesses are consistent with those of the MR. Analysis based on second harmonic generation, terahertz emission, Seebeck/Hall effects, Raman scattering, X-ray diffraction, and X-ray photoemission demonstrates that the Dirac- to Weyl-semimetal phase transition for films thinner than ≈10 nm is induced by inversion-symmetry breaking due to the lattice-mismatch strain between the Bi0.96Sb0.04 film and substrate. The realization of 2D WSMs is particularly significant for applications in high-speed electronics, spintronics, and quantum computations due to their high mobility, chiral spin, and topologically-protected quantum qubits.