The spatiotemporal relaxation of electrons in spatially one-dimensional plasmas acted upon by electric fields is investigated on the basis of the space- and time-dependent electron Boltzmann equation. The relaxation process is treated using the two-term approximation of an expansion of the electron velocity distribution function in Legendre polynomials. To verify the complex Boltzmann equation approach by a completely independent kinetic method, results for inhomogeneous column-anode plasmas of glow discharges between plane electrodes are compared with corresponding ones obtained by Monte Carlo simulations. The spatiotemporal electron relaxation in argon plasmas, subjected to a space-independent electric field and maintained by a time-independent inflow of electrons at the cathode side of the plasma region, is considered. Starting from steady state at a given electric field, the relaxation process is initiated by a pulse-like change of the electric field strength and is traced until the spatially structured, time-independent state associated to the changed field is reached. The behaviour of the velocity distribution function and macroscopic quantities of the electrons in space and time is analyzed for enlarged and reduced electric field strengths typical of the column region of glow discharges. In particular, the spatiotemporal reformation of plasma structures has been found to progress in two phases, i.e., existing structures in the distribution are driven to merge in wide plasma region first, followed by a formation phase of new spatial structures which are induced by the cathode-sided inflow of electrons. The results for the macroscopic quantities and the isotropic distribution functions obtained by Boltzmann and Monte Carlo calculations agree very well during the spatiotemporal transient process as well as in the new steady state finally reached.