The self-consistent full-potential total-energy Korringa-Kohn-Rostoker electronic-structure method is generalized to include all relativistic effects. The Dirac equation for a general anisotropic 4\ifmmode\times\else\texttimes\fi{}4 potential is solved inside Voronoi polyhedra surrounding each basis atom. As an illustration, the method is used to calculate the self-consistent electronic band structure, the Fermi surface, the equilibrium lattice constant and the bulk modulus of the fcc transition metals Pd, Ir, Pt, and Au. If the cutoff of the multipole expansions of the wave functions is at least ${\mathit{l}}_{\mathrm{max}}$=4, the calculated equilibrium lattice constants of the transition metals deviate from experiment by less than 1%, and the calculated bulk moduli deviate between 6% and 20%, which is comparable to results of other local-density calculations. In addition, the method is used to calculate the self-consistent electronic band structure of the semiconductors GaAs, InSb, and InN, and the equilibrium lattice constant and the bulk modulus of InSb. We find that the inclusion of both spin-orbit coupling and full-potential effects influences the size of the valence-band-width and the band gap in comparison with scalar relativistic local-density calculations. Interestingly, if after self-consistency has been achieved in scalar relativistic calculations, spin-orbit coupling is taken into account by the so-called second variation, the energy bands are found to agree very well with the results obtained here with the full relativistic treatment. \textcopyright{} 1996 The American Physical Society.