The accurate prediction of electrokinetic migration velocity and dispersion is crucial to separating electrophoretically charged solutes in micro- or nanochannels. In this paper, we investigate numerically the influence of transverse electromigration (TEM) on the solute electrokinetic transport in a series of micro- and nanochannels. The TEM, often ignored in previous studies, is demonstrated to significantly affect the solute migration velocity in nanochannels and the electrokinetic dispersion in microchannels. This is because the TEM can force either positively charged solutes into or negatively charged solutes out of the electrical double layer that forms adjacent to the negatively charged channel wall and contains the velocity gradients. Analytical solutions are also derived for characterizing the electrokinetic transport of charged solutes in nanochannels, which has been validated to be in good agreement with the numerical simulation. Moreover, we demonstrate that the proposed analytical formula for the solute migration velocity actually applies to channels of any size.