We develop a new and numerically efficient formalism to describe the general problem of the scattering and absorption of light by a spherical metal or dielectric particle illuminated by a tightly focused beam. The theory is based on (i) the generalized Mie theory equations, (ii) the plane-wave decomposition of the converging light beam, and (iii) the expansion of a plane wave in terms of vector spherical harmonics. The predictions of the model are illustrated in the case of silver nanoparticles. The results are compared with the Mie theory in the local approximation. Finally, some effects related to the convergence of the beam are analyzed in the context of experiments based on the spatial modulation spectroscopy technique.