We propose a model for solvated positronium (Ps) atoms in water, based on the sequential quantum mechanics/molecular mechanics (s-QM/MM) protocol. We developed a Lennard-Jones force field to account for Ps-water interactions in the MM step. The repulsive term was obtained from a previously reported model for the solvated electron, while the dispersion constant was derived from the Slater-Kirkwood formula. The force field was employed in classical Monte Carlo (MC) simulations to generate Ps-solvent configurations in the NpT ensemble, while the quantum properties were computed with the any-particle molecular orbital method in the subsequent QM step. Our approach is general, as it can be applied to other liquids and materials. One basically needs to describe the solvated electron in the environment of interest to obtain the Ps solvation model. The thermodynamical properties computed from the MC simulations point out similarities between the solvation of Ps and noble gas atoms, hydrophobic solutes that form clathrate structures. We performed convergence tests for the QM step, with particular attention to the choice of basis set and expansion centers for the positronic and electronic subsystems. Our largest model was composed of the Ps atom and 22 water molecules in the QM region, corresponding to the first solvation shell, surrounded by 128 molecules described as point charges. The mean electronic and positronic vertical detachment energies were (4.73 ± 0.04) eV and (5.33 ± 0.04) eV, respectively. The latter estimates were computed with Koopmans' theorem corrected by second-order self-energies, for a set of statistically uncorrelated MC configurations. While the Hartree-Fock wave functions do not properly account for the annihilation rates, they were useful for numerical tests, pointing out that annihilation is more sensitive to the choice of basis sets and expansion centers than the detachment energies. We further explored a model with reduced solute cavity size by changing the Ps-solvent force field. Although the pick-off annihilation lifetimes were affected by the cavity size, essentially the same conclusions were drawn from both models.