The median Doppler shift of radar echoes is analyzed in measurements by ENVISAT's Advanced Synthetic Aperture Radar (ASAR) over the ocean. This Doppler centroid differs from a predicted signal based on the predicted motion of the satellite and Earth. This anomaly, converted to a surface Doppler velocity UD, appears to be of geophysical origin. Two wide-swath images over the Gulf Stream around Cape Hatteras suggest that UD contains high-resolution information on surface currents, while on a global scale, UD is found to vary with the wind speed in the range direction. A simple quantitative forward model is proposed, based on a practical two-scale decomposition of the surface geometry and kinematics. The model represents the effect of the wind through the wave spectrum, and gives UD ≈ γU10$parallel$ + Uc$parallel$, with U10$parallel$ and Uc$parallel$ as the 10 m wind speed and quasi-Eulerian current in the line of sight of the radar projected on the sea surface, respectively, and γ as a coefficient function of the wind speed, wave development, and radar geometry. It is found that for an incidence angle of 23¿, γ ≈ 0.3 for moderate winds and fully developed seas. This model is validated with a global data set of ASAR Wave Mode observations, with colocated model winds, acquired over the global ocean during the years 2003 and 2004. The Doppler signal therefore provides the signed parameter UD that can be used to reduce the wind direction ambiguity in the inversion of high-resolution wind fields from SAR imagery. A qualitative validation of current effects is shown for the English Channel where tidal currents dominate. Thus it should be possible to combine this previously ignored geophysical Doppler signal with traditional information on sea surface roughness, in order to provide very high resolution wind and current fields.