We present the first calculation of the kinetic Sunyaev-Zeldovich (kSZ) effect due to the inhomogeneous reionization of the universe based on detailed large-scale radiative transfer simulations of reionization. The resulting sky power spectra peak at l=2000-8000 with maximum values of l^2C_l~1times10^{-12}. The peak scale is determined by the typical size of the ionized regions and roughly corresponds to the ionized bubble sizes observed in our simulations, ~5-20 Mpc. The kSZ anisotropy signal from reionization dominates the primary CMB signal above l=3000. This predicted kSZ signal at arcminute scales is sufficiently strong to be detectable by upcoming experiments, like the Atacama Cosmology Telescope and South Pole Telescope which are expected to have ~1 resolution and ~muK sensitivity. The extended and patchy nature of the reionization process results in a boost of the peak signal in power by approximately one order of magnitude compared to a uniform reionization scenario, while roughly tripling the signal compared with that based upon the assumption of gradual but spatially uniform reionization. At large scales the patchy kSZ signal depends largely on the ionizing source efficiencies and the large-scale velocity fields: sources which produce photons more efficiently yield correspondingly higher signals. The introduction of sub-grid gas clumping in the radiative transfer simulations produces significantly more power at small scales, and more non-Gaussian features, but has little effect at large scales. The patchy nature of the reionization process roughly doubles the total observed kSZ signal for l~3000-10^4 compared to non-patchy scenarios with the same total electron-scattering optical depth.
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