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We present a first-principles model to study tunnel transistors based on van der Waals heterojunctions of 2D materials in the presence of dissipative mechanisms due to the electron-phonon interaction. To this purpose we employed a reduced basis set composed of unit-cell restricted Bloch functions computed with a plane wave ab-initio solver and performed self-consistent quantum transport simulations within the non-equilibrium Green’s functions formalism. Phonon scattering was included with specific self-energies making use of the deformation potential approximation for the electron-phonon coupling. Our simulations identify the van der Waals tunnel FET as a promising option to attain high on-state currents at low supply voltages, but also show a strong impact of the phonon scattering on the transport properties of such device in the sub-threshold regime.