Optical (R) and near-infrared (K') images of the IRAS 1-Jy sample of 118 ultraluminous infrared galaxies have been studied. All but one object in the 1-Jy sample show signs of strong tidal interaction/merger. Most of them harbor a single disturbed nucleus and are therefore in the later stages of a merger event. Single-nucleus ULIGs show a broad distribution in host magnitudes with significant overlap with those of quasars. The same statement applies to R - K' colors in ULIG and quasar hosts. An analysis of the surface brightness profiles of the host galaxies in single-nucleus sources reveals that about 35% of the Rand K' surface brightness profiles are well fit by an elliptical-like R1/4-law, while only 2% are well fit by an exponential disk. Another 38% of the single-nucleus systems are fit equally well with an exponential or de Vaucouleurs profile. Elliptical-like hosts are most common among merger remnants with Seyfert 1 nuclei (83%) and Seyfert 2 optical characteristics (69%). The mean effective radius of these ULIGs is 4.80 ± 1.37 kpc at R and 3.48 ± 1.39 kpc at K'. These values are in excellent agreement with recent quasar measurements obtained at H with HST. The hosts of elliptical-like 1-Jy systems follow with some scatter the same μe - re relation, giving credence to the idea that some of these objects may eventually become elliptical galaxies if they get rid of their excess gas or transform this gas into stars.