The recent VINCI/VLTI observations presented in Paper I have nearly doubled the total number of available angular diameter measurements of Cepheids. Taking advantage of the significantly larger color range covered by these observations, we derive in the present paper high precision calibrations of the surface brightness-color relations using exclusively Cepheid observations. These empirical laws make it possible to determine the distance to Cepheids through a Baade-Wesselink type technique. The least dispersed relations are based on visible-infrared colors, for instance FV(V-K) = -0.1336 ± 0.0008 (V-K) + 3.9530 ± 0.0006}. The convergence of the Cepheid (this work) and dwarf star (Kervella et al. \cite{kervella04c}) visible-infrared surface brightness-color relations is strikingly good. The astrophysical dispersion of these relations appears to be very small, and below the present detection sensitivity. Table \ref{table_measurements1} is only available in electronic form at http://www.edpsciences.org