A hybrid thermodynamic and density-functional theory for heterogeneous nucleation on mesoscopic wettable particles is developed. The nonlocal density-functional theory (DFT) is on basis of the weighted-density approximation (WDA) of Tarazona. The model system consists of a Lennard-Jones (LJ) fluid and a 9-3 LJ wall for the solid particle. Effects of the droplet curvature and compressibility are accounted for in the theory. A by-product of this work is the calculation of the Tolman length using the WDA-DFT (Appendix A). Important characteristics of the heterogeneous nucleation, including the chemical potential of the liquid condensate, the free energy of droplet formation, and the barrier height to nucleation, are obtained.