Electroosmotic flow is widely used as a primary method of species transport in microfluidic devices. The recent introduction of several alternating current (ac) based microfluidic applications has led to enhanced interest in time periodic electroosmotic flows. In this work, an analytical solution, via a Green's function formulation, is developed for ac electroosmotic flow through a rectangular microchannel for the case of a sinusoidal applied electric field. The response of the flow field to excitation by more complex waveforms is also investigated using numerical simulations. It is shown that the steady time periodic (after the effects of the initial impulse are dissipated) velocity profile is characterized by the ratio of the period of oscillation to the time scale for viscous diffusion, by the surface zeta-potential distribution, and by the channel aspect ratio. Impulsively started flows are also shown to exhibit interesting transient behavior resulting in a net positive velocity at the channel midpoint during the initial cycles prior to reaching the steady state oscillation. The influence of the particular excitation waveform is demonstrated to be more significant at lower frequencies since the bulk flow has more time to respond to instantaneous changes in the applied potential.