This paper describes an innovative approach to estimate motion from image observations of divergence-free flows. Unlike most state-of-the-art methods, which only minimize the divergence of the motion field, our approach utilizes the vorticity-velocity formalism in order to construct a motion field in the subspace of divergence free functions. A 4DVAR-like image assimilation method is used to generate an estimate of the vorticity field given image observations. Given that vorticity estimate, the motion is obtained solving the Poisson equation. Results are illustrated on synthetic image observations and compared to those obtained with state-of-the-art methods, in order to quantify the improvements brought by the presented approach. The method is then applied to ocean satellite data to demonstrate its performance on the real images.