In this work a Vortex Particle Method is combined with a Boundary Element Method for the study of viscous incompressible planar flow around solid bodies. The method is based on Chorin’s operator splitting approach, consisting of an advection step followed by a diffusion step. The evaluation of the advection velocity exploits the Helmholtz-Hodge Decomposition, while the no–slip condition is enforced by an indirect boundary integral equation. No mesh is used for the solution of the Poisson equation for the velocity (advection step) and the diffusion step is performed on a Regular Point Distribution with no topological connection; therefore, the resulting algorithm is completely meshless. We also revise the use of the same decomposition for the solution of the Navier–Stokes equations in primitive variables and its role in maintaining the divergence–free constraint. The results are compared with those obtained by a mesh-based Finite Volume Method, where the pseudo-compressible iteration is exploited to enforce the solenoidal constraint on the velocity field. Several benchmark tests were performed for verification and validation purposes; in particular, the unsteady flow past a circular cylinder, an ellipse with incidence and an equilateral triangle was simulated for several values of the Reynolds number.