We investigate the wind-driven current response over the world ocean using SVP drifting buoys, ERS-1 and ERS-2, and TOPEX altimetry data and ECMWF wind stress fields. Wind-driven ageostrophic currents are estimated from drifting buoys by removing altimetry deduced geostrophic currents from observed drifting velocities. Removing the geostrophic signal enhances the coherence with wind stress at periods longer than 10 days. For superinertial periods lower than 20 days, a two-parameter (i.e., angle and amplitude) model is fitted to the isolated ageostrophic signal to study the upper ocean response to surface wind stress in that frequency band. The model, which can explain up to 30% of the variance in some areas, indicates that the currents spiral to the right (left) of the wind with depth in the Northern (Southern) Hemisphere, in agreement with the Ekman theory. The absolute value of the angle parameter is found to exhibit significant spatial and seasonal variability. The vertical eddy viscosity and the Ekman layer depth as deduced from Ekman theory are compared to previous results. Their seasonal variability is also studied. Model results are then used to compute the mean and standard deviation of ageostrophic currents in 5¿ boxes over the world ocean. The equatorial divergence and the subpolar and subtropical convergence zones are well reproduced.