The interaction between free-surface waves and localized vorticity structures is a fundamental problem in fluid dynamics, with relevance to geophysical flows. We study this problem by using the general framework for 2D water waves with arbitrary vorticity developed by Ionescu-Kruse and Ivanov (JDE, 2023). In the small-amplitude long-wave Boussinesq and KdV regimes, we derive coupled evolution equations for the free surface and the vortex dynamics. Our analysis shows that the interaction with the vortex does not destroy the surface solitary waves and, for a significant range of the vortex strength, the solitary waves remain practically unaffected. This observation leads to a further simplification of the model, in which the vortex motion beneath propagating solitons is described by a decoupled system of ODEs, capturing the qualitative features of the interaction. Analytical results are complemented by numerical simulations (see Ionescu-Kruse, Ivanov, Todorov, J. Nonlinear Sci, 2026).