Satellite altimetry offers a unique approach for direct sea surface current observation, but it is limited to measuring the surface‐constrained geostrophic component. Ageostrophic dynamics, prevalent at horizontal scales below 100 km and time scales below 10 days, are often underestimated by ocean reanalyzes employing data assimilation schemes. To address this limitation, we introduce a novel deep learning scheme, rooted in a variational data assimilation formulation with trainable observations and a priori terms, that harnesses the synergies between satellite‐derived sea surface observations, namely sea surface height (SSH) and sea surface temperature (SST), to enhance sea surface current reconstruction. Numerical experiments, conducted using realistic simulations, in a case study area of the Gulf Stream, demonstrate the potential of the proposed scheme to capture ageostrophic dynamics at time scales of 2.5–3.0 days and horizontal scales of 0.5°–0.7°. The analysis of diverse observation configurations, encompassing nadir along‐track altimetry, wide‐swath SWOT (Surface Water and Ocean Topography) altimetry, and SST data, highlights the pivotal role of SST features in retrieving a significant portion of the ageostrophic dynamics (approximately 47%). These findings underscore the potential of deep learning and 4DVarNet schemes in improving ocean reanalyzes and enhancing our understanding of ocean dynamics.