Deep VLT optical spectroscopy, HST+ACS (GOODS) imaging and VLA observations are used to unveil the nature of a complete sample of 47 EROs with R-Ks>5 and Ks<20. The spectroscopic redshift completeness is 62%. Morphological classification was derived for each ERO through visual inspection and surface brightness profile fitting. Three main ERO morphological types are found: E/S0 galaxies (30-37%), spiral-like (24-46%) and irregular systems (17-39%). The only ERO detected in the radio is likely to host an obscured AGN. The average radio luminosity of the star-forming EROs undetected in the radio implies star formation rates of the order of 33 Msun yr^-1. The colors, redshifts and masses of the E/S0 galaxy subsample imply a minimum formation redshift z_f ∼ 2. With this z_f there is enough time to have old and massive stellar spheroids already assembled at z ∼ 1. We verify that the R-Ks vs. J-Ks color diagram is efficient in segregating old and dusty-star-forming EROs. Comment: 5 pages, 5 figures, to appear in Astronomy & Astrophysics Letters