Nucl.Phys.B724:3-182,2005 We compute the full three-loop coefficient functions for the structure functions F_2 and F_L in massless perturbative QCD. The results for F_L complete the next-to-next-to-leading order description of unpolarized electromagnetic deep-inelastic scattering. The third-order coefficient functions for F_2 form, at not too small values of the Bjorken variable x, the dominant part of the next-to-next-to-next-to-leading order corrections, thus facilitating improved determinations of the strong coupling alpha_s from scaling violations. The three-loop corrections to F_L are larger than those for F_2. Especially for the latter quantity the expansion in powers of alpha_s is very stable, for photon virtualities Q^2 >> 1 GeV^2, over the full x-range accessible to fixed-target and collider measurements.