A simplified analytical model is developed to describe the baroclinic and barotropic ocean response to moving Tropical cyclones (TC) and their associated pycnocline erosions. The model builds on classical mixed layer (ML) models and linear models of ocean response to transient events. As suggested, disturbances of the upper ocean stratification caused by the ML development shall not strongly impact the dynamics of baroclinic modes. Accordingly, the baroclinic response can be estimated using the pre‐storm ocean stratification condition. To the contrary, the ML is strongly coupled with these interior motions, through the TC‐induced upwelling response which affects the entrainment velocity. The ML temperature is then strongly dependent on the local temperature gradient in the upper layer. The model is represented by a set of analytical relationships providing rapid calculations for the ocean response to TC, given a prescribed wind velocity field traveling over an ocean with arbitrary stratification. Compared to satellite observations, simulations demonstrate the model ability to quantitatively reproduce the observed shape and magnitudes of the sea surface height (SSH) and the surface temperature (SST) anomalies. Remarkably, the model is robust and efficient for a wide range of variability of TC characteristics (max wind speed, radius, shape of wind profile, translation velocity), parameters of the ocean stratification, and Coriolis parameter. Simulations provide solid evidences about the key role of TC‐induced upwelling in the ML cooling and formation of SST wake. Cross‐track advection by wind driven currents, though small compared with TC translation velocity, can significantly contribute to broaden the shape and offset of the SST wake. Given its effectiveness and low computational burden, the proposed model can be introduced as a computational module into atmospheric numerical models of TC coupled‐evolution with the ocean, through the resulting local changes of surface enthalpy fluxes.