We study the mechanism of lattice parameter accommodation and the structure of GaAs nanowires (NWs) grown on Si(111) substrates using the Ga-assisted growth mode in molecular beam epitaxy. These nanowires grow preferentially in the zincblende structure, but contain inclusions of wurtzite at the base. By means of grazing incidence x-ray diffraction and high-resolution transmission electron microscopy of the NW-substrate interface, we show that the lattice mismatch between the NW and the substrate is released immediately after the beginning of NW growth through the inclusion of misfit dislocations, and no pseudomorphic growth is obtained for NW diameters down to 10 nm. NWs with a diameter above 100 nm exhibit a rough interface towards the substrate, preventing complete plastic relaxation. Consequently, these NWs exhibit a residual compressive strain at their bottom. In contrast, NWs with a diameter of 50 nm and below are completely relaxed because the interface is smooth.