Surface ocean circulation shapes climate, air-sea exchange, and the transport of heat, carbon, and other tracers, yet most long-term satellite-based global datasets rely primarily on geostrophic balance and therefore miss important ageostrophic motions. Here, we reconstruct global daily sea surface circulation at 0.25° resolution from 1993 to 2023 using a physics-informed deep learning framework that integrates satellite altimetry with momentum constraints from geostrophic balance, wind stress, and nonlinear advection. The resulting dataset is dynamically consistent, with a mean momentum-balance error below 1.5 %, and reduces the median velocity error against independent mooring observations to 0.07 m s⁻¹, compared with 0.20 m s⁻¹ for geostrophic currents and 0.10 m s⁻¹ for Ekman-corrected currents. We show that geostrophic flow sets the large-scale circulation, whereas Ekman and nonlinear contributions are smaller but comparable in magnitude to each other. Although nonlinear advection contributes little to relative vorticity, it strongly shapes surface divergence and the fine-scale structure of eddy kinetic energy. Our results show that nonlinear ageostrophic flow is an essential component of global surface circulation and that neglecting it limits our ability to resolve surface transport and variability on climatically relevant scales.